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Masonry and 
Reinforced Concrete 



A Working Manual of 

APPROVED AMERICAN PRACTICE IN THE SELECTION, TESTING, AND 
STRUCTURAL USE OF BUILDING STONE, BRICK, CEMENT, AND 
OTHER MASONRY MATERIALS, WITH COMPLETE IN- 
STRUCTION IN THE VARIOUS MODERN STRUC- 
TURAL APPLICATIONS OF CONCRETE 
AND CONCRETE STEEL 



By WALTER LORING WEBB, C. E. 

Consulting Civil Engineer; Author of "Railroad Construction," 
"Economics of Railroad Construction," etc. 



and 
W. HERBERT GIBSON, B. S., C. E. 

Civil Engineer 
Designer of Reinforced Concrete 



ILLUSTRATED 



CHICAGO 
AMERICAN SCHOOL OF CORRESPONDENCE 
x, 1909 



<\ 



fc 









LIBRARY of CONGRESS 
TwoCeoies Revived 

JAN 13 1909 

OWSS dJxXc.no. 
OOPV 3. 



Copyright 1908 by 
American Schooi, of Correspondence; 



Entered at Stationers' Hall, London 
All Rig-hts Reserved 










Foreword 



THE oldest constructive works made by man, of which 
there is any present evidence, were made of some form 
of plain masonry. The Egyptians accomplished work 
which has never been surpassed— and perhaps has not been 
equaled — in the construction of masonry involving the use of 
enormous blocks of stone. A cementing material which would 
not only fill the joints between the stones but was also used to 
make a form of concrete, was invented at a very early period. 
Some of this concrete work is still in existence, and is an un- 
answerable argument as to the durability of concrete, although 
the art of making cement was not understood then as it is now. 

C. But at this point progress appeared to stop for two or three 
thousand years. The construction of deep and sub-aqueous 
foundations, and the scientific and economical design of arches 
and retaining walls, have been developed only during the last 
few years. The possibility of combining in reinforced concrete 
the durability of masonry and the power of steel to resist ten- 
sion and shearing (which is afforded by the reinforcing metal 
in the concrete) , has resulted in the substitution of reinforced 
concrete for plain steel in structures which are especially sub- 
ject to deterioration. There are many structures— such as high 
buildings and bridges of considerable span — which, before the 
invention of reinforced concrete, were made of steel, because 



that appeared to be the only practicable material; but now re- 
inforced concrete is displacing the use of plain steel as the 
structural material. 

C. There is therefore little danger in over-estimating the impor- 
tance of a method of construction which has had such a wonder- 
ful development in recent years, and which will probably be 
developed still more during the coming years. 

C. Not only has there been an advance in the character of the 
work that can be done, but there has also been a great improve- 
ment in methods of work, which has resulted in economy in the 
cost of construction. These practical methods of work, particu- 
larly in reinf orced-concrete construction, have been given special 
attention in this volume, and the student will find this feature 
of the book to be of particular value at this time. 

Walter Loring Webb 
W. Herbert Gibson 




Table of Contents 



Masonry and Concreting Materials Page 1 

Properties of Natural Stone — Stone Testing — Building Stone (Limestone, Mar- 
ble, Sandstone, etc.) — Brick — Concrete Blocks — Lime — Cements (Slag, Nat- 
ural, Portland) — Cement Testing — Sand — Broken Stone — Mortar — Propor- 
tions for Mixing Mortar and Concrete — Compressive, Tensile, and Shearing 
Strength of Concrete — Wetness — Transporting and Depositing— Bonding — 
Effects of Freezing — Waterproofing — Preservation of Steel in Concrete — 
Fire Protection — Hand and Machine Mixing — Reinforcing Steel — Plain and 
Deformed Bars — Expanded Metal 



Stone Masonry and Plain Concrete Construction . . Page 

Glossary of Terms — Stone Cutting and Dressing (Ashlar, Squared Stone, etc.)- 
— Constructive Features (Bonding, Amount of Mortar, etc.) — Brick Masonry 
— Cost of Stone and Brick Work — Common, English, and Flemish Bond — 
Measuring Brickwork — Efflorescence — Depositing Concrete under Water — Clay 
Puddle — Foundation Work — Footings— Pile Foundations — Piles — Pile-Shoes — 
Pile-Driving — Concrete Piles (Raymond, Simplex, etc.) — Cost of Piling — 
Cofferdams — Cribs — Caissons (Open, Pneumatic, etc.) — Retaining Walls — 
Methods of Failure — Bridge Piers and Abutments — Culverts — Concrete Walks 
and Curbing 



Reinforced Concrete „ Page 173 

General Theory of Flexure — Statics of Plain Homogeneous Beams — Concrete 
in Compression and Steel in Tension — Elasticity of Concrete — Analysis and 
Composition of Compressive Forces — Neutral Axis — Percentage of Steel — 
Resisting Moment — Useful Formula? — Slab and Beam Computations — Resist- 
ance to Slipping of Steel — Bond Required in Bars — Guarding against Failure 
by Diagonal Tension — Design of Plain Beam — Quality of Steel — Reinforced 
Slabs — Temperature Cracks — Strength of T-Beams — Width of Flange and 
Rib — T-Beam Formula? — Shearing Stresses in Beams and Slabs — Computa- 
tion of Simple and Beam Footings — Retaining Walls — Wind Bracing — Vertical 
Walls — Culverts (Box, Arch) — Design of Columns — Eccentric Loading — 
Water Tanks — Finishing Concrete Surfaces — Mouldings and Ornamental 
Shapes — Use of Colors — Efflorescence and Laitance — Machinery for Concret- 
ing — Mixers (Gravity, Rotary, Paddle) — Automatic Measures — Engines, 
Motors, Hoists, etc. — Plant for a 10-Story Building — Plant for Street Work 
— Block Machines — Forms (for Columns, Sewers, Walls, etc.) — Cost of 
Forms — Collapsible Steel Forms — Centers for Arches — Safe Stresses in 
Wooden Forms — Safe Loads on Wooden Columns — Bending or Trussing Bars 
— Bonding Old and New Concrete — Representative Structures (Office Build- 
ings. Shops, Sewers, Bridges, etc.) — Theory of Arches — Composition of 
Forceps — Equilibrium Polygons — Glossary of Terms — Kinds of Arches — 
Statics of Youssoir Arches — Depth of Keystone — Reduced Load Line — Com- 
putation of Loads — Correcting an Arch Design — Design of Abutments — 
Oblique Forces on Arches — Stability of Piers — Elastic Arches — Application of 
Calculus — Classification of Arch Ribs — Arch Computations 



Index . . . Page 431 




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MASONRY AND REINFORCED 
CONCRETE 

PART I 



MASONRY MATERIALS 

Masonry may be defined as construction in which the chief 
constructive material is stone or an artificial mineral product such 
as brick, terra-cotta, or cemented blocks. Under this broad defini- 
tion, even Reinforced Concrete may be considered as a specialized 
form of masonry construction. 

NATURAL STONE AND ITS CHARACTERISTICS 

1. From the constructor's standpoint, any stone is good which 
will fulfil certain desired characteristics. These various charac- 
teristics are not found combined in the highest degree in any one 
kind of stone. It is essential to learn to what extent these various 
desirable characteristics are combined in the various types of stone 
which are quarried. At the same time, it should not be forgotten 
that stones of the same nominal classification vary greatly in the 
extent of their desirability. The chief characteristics to be con- 
sidered by the constructor are Cost, Durability, Strength, and Appear- 
ance. Although in some cases this represents the order in which 
these qualifications are desired, in other cases the order is indefinitely 
varied. For example, in a high-grade public building or monument, 
a good appearance is considered essential, regardless of cost. In a 
subsurface foundation, appearance is of absolutely no importance. 

2. Cost. The cost of any stone depends on its intrinsic valua- 
tion in the quarry, the cost of quarrying and dressing, and the 
cost of transportation from the quarry to the site of the structure. 
The cost of transportation is often the most important, and this 
consideration frequently decides not only the choice of stone but even 
the type of construction — whether stone masonry or concrete. To 
give a rough idea of the cost of stone quarrying, a few values are 

Copyright, 1908, by American School of Correspondence, 



2 MASONRY AND REINFOKCED CONCRETE 

quoted from Gillette's "Handbook of Cost Data." In one instance 
the cost of quarrying granite, exclusive of rental of plant, rental of 
quarry, and cost of stripping off the upper soil, averaged about $4.50 
per cubic yard. In another instance the cost of quarrying rubble 
amounted to $1.80 per cubic yard. The cost of explosives was not 
included in this estimate, but it should not have increased the cost to 
over $2.00 per cubic yard. In another instance the cost of quarrying 
gneiss amounted to $3.55, not including explosives and teaming. 
Even these items should not have made the total cost more than 
$4.25 per cubic yard. 

3. Durability. Under many conditions the most important 
qualification is durability. The lack of it is also the most seriously 
disappointing quality. Rocks which have remained hard and tough 
for unnumbered ages while covered by earth from air and frost, will 
disintegrate after a comparatively few years' exposure. 

Atmospheric Influences. A very porous stone will absorb water, 
which may freeze and cause crystals near the surface to flake off. 
Even though such action during a single winter may be hardly per- 
ceptible, the continued exposure of fresh surfaces to such action may 
sooner or later cause a serious loss and disintegration. Even rain 
water which has absorbed carbonic acid from the atmosphere will 
soak into the stone, and the acid will have a greater or less effect on 
nearly all stones. Quartz is the only constituent which is absolutely 
unaffected by acid. The sulphuric acid gas given off by coal will 
also affect building stone very seriously. 

Fire. Natural stone is far less able to withstand a conflagration 
than the artificial compositions such as brick, concrete, and terra- 
cotta. Granite, so popularly considered the type of durability, is 
especially affected. Limestone and marble will be utterly spoiled, 
at least in appearance if not structurally, by a hot fire. Sandstone 
is the least affected of the natural stones. 

Hardness. The durability of a stone is tested by its resistance 
to abrasive action in pavements, door-sills, and similar cases. The 
value of trap rock for macadam and block pavements is chiefly due 
to this quality. 

4. Strength. In some structural work (as, for example, an 
arch) the crushing strength of the stone is the primary consideration. 
The average crushing strength of various kinds of stone will be 



MASONRY AND REINFORCED CONCRETE 3 

quoted later. The tensile strength should never be depended on, 
except to a very limited extent as a function of the transverse strength. 
Even this is only applicable to such cases as the lintels over doors 
and windows, the footing stones for foundations, and the cover stones 
for box culverts. It is usually true that a stone which is free from 
cracks and which has a high crushing strength also, has as much 
transverse strength as should be required of any stone. 

5. Appearance. It is seldom that an engineer need concern 
himself with the appearance of a stone, provided it is satisfactory in 
the respects previously mentioned. The presence of iron oxide in 
a stone will sometimes cause a deterioration in appearance by. the 
formation of a reddish stain on the outer surface. It usually happens, 
however, that a stone whose strength and durability are satisfactory 
will have a sufficiently good appearance, unless in high-grade archi- 
tectural work, where it is considered essential that a certain color 
or appearance shall be obtained. 

TESTING STONE 

6. Of the above four qualities, only two — durability and 
strength — are susceptible of laboratory testing, and even for these 
qualities the best known laboratory tests are not conclusive. The 
deterioration and partial failure of the masonry in some of the best 
known cathedrals of Europe, which commanded the best available 
talent in their construction, are startling illustrations of the imprac- 
ticability of determining from laboratory tests the effect on stone of 
long-continued stress, combined perhaps with other destructive 
influences. Although the best technical advice was obtained in 
selecting the stone for the Parliament House in London, and the 
stone selected was undoubtedly subjected to the best known tests, it 
was apparently impossible to foresee the effect of the London atmos- 
phere, which is now so seriously affecting the stone. Several of the 
tests to be described below should be considered as being negative 
tests. If the stones fail under these tests, they are probably inferior; 
if they do not fail, they are perhaps safe, but there is no certainty. 
A long experience, based on a knowledge of the characteristics of 
stones which have proven successful, is of far greater value than a 
dependence on the results of laboratory tests. The tests attempt to 
simulate the actual destructive agencies as far as possible, but since 



4 MASONRY AND REINFORCED CONCRETE 

a great deal of stonework which was apparently satisfactory when 
constructed and for a few years after, has failed for a variety of 
reasons, attempts are made to use accelerated tests, which are supposed 
by their concentration to affect the stone in a few minutes or hours 
as much as the milder causes acting through a long period of years. 

7. Absorption. It is generally said that stones having the 
least absorption are the best. The absorptive power is measured by 
first drying the stone for many hours in an oven, weighing it, then 
soaking it for, say, 24 hours, and again weighing it. The increase 
in the weight of the soaked stone (due to the weight of water ab- 
sorbed), divided by the weight of the dry stone, equals, the ratio of 
absorption. The granites will absorb as an average value a weight 
of water equal to about T ^ of the weight of the stone. For sand- 
stone the ratio is about ^t- 

The test for absorption has but little value except to indicate 
a closeness of grain (or the lack of it), which probably indicates some- 
thing about the strength of the stone, as well as its liability to some 
kinds of disintegration,, 

8. Test for Frost. The only real test is to wash, dry, and weigh 
test specimens, very carefully; then soak them in water, and expose 
them to intensely cold and intensely warm temperatures alternately. 
Finally wash, dry, and weigh them. If the freezing has resulted in 
breaking off small pieces, or possibly in fracturing the stone, the loss 
in weight or the breakage will give a measure of the effect of cold 
winters. However, as such low temperatures cannot be produced 
artificially except at considerable expense, and as a sufficient degree 
of cold is ordinarily unobtainable when desired, such a test is Usually 
impracticable. 

An attempt to simulate such an effect by boiling the specimen in 
a concentrated solution of sulphate of soda and observing the subse- 
quent disintegration of the stone, if any, is known as Brard's test. 
Although this method is much used for lack of a better, its value is 
doubtful and perhaps deceptive, since the effect is largely chemical 
rather than mechanical. The destructive effect on the stone is 
usually greater than that of freezing, and might result in condemning 
a really good stone. 

9. Chemical Test. The most difficult and uncertain matter 
to determine is the probable effect of the acids in the atmosphere. 



MASONRY AND REINFORCED CONCRETE 5 

These acids, dissolved in rain water, soak into the stone and combine 
with any earthy matter in the stone, which then leaches out, leaving 
small cavities. This not only results in a partial disintegration of 
the stone, but also facilitates destruction by freezing. If the stone 
specimen, after being carefully washed, is soaked for several days in 
a one per cent solution of sulphuric and hydrochloric acid, the liquid 
being frequently shaken, the water will become somewhat muddy 
if there is an appreciable amount of earthy matter in the stone. Such 
an effect is supposed to indicate the probable action of a vitiated 
atmosphere. Of course it should be remembered that such a con- 
sideration is important only for a structure in a crowded city where 
the atmosphere is vitiated by poisonous gases discharged from fac- 
tories and from all chimneys. 

10. Physical Tests. A test made by crushing a block of stone 
in a testing machine is apparently a very simple and conclusive test, 
but in reality the results are apt to be inconclusive and even decep- 
tive. This is due to the following reasons, among others: 

(a) The crushing strength of a cube per square inch is far less than 
that of a slab having considerably greater length and width than height. 

(b) The result of a test depends very largely on the preparation of 
the specimen. If sawed, the strength will be greater than if cut by chipping. 
If the upper and lower faces are not truly parallel, so that there is a concen- 
tration of pressure on one corner, the apparent result will be less. 

(c) The result depends on the imbedment. Specimens which are 
rubbed and ground with machines that will insure truly parallel and plane 
surfaces, will give higher results than when wood, lead, leather, or plaster- 
of-paris cushions are employed. 

(d) The strength of masonry depends largely on the crushing strength 
of the mortar used and the thickness of the joints. Other things being equal, 
an increase in the crushing strength of the stone (or brick) which is used 
does not add proportionately to the strength of the masonry as a whole; 
and if the mortar joints are very thick, it adds little or nothing. Since the 
strength of the masonry is the only real criterion, the strength of a cube of 
the stone is of comparatively little importance. 

In short, tests of two-inch cubes (the size usually employed) are 
valuable chiefly in comparing the strength of two or more different 
kinds of stones, all of which are tested under precisely similar con- 
ditions. A comparison of such figures with the figures obtained by 
others will have but little value unless the precise conditions of the 
other tests are accurately known. Under any conditions, the results of 



MASONRY AND REINFORCED CONCRETE 



the tests will bear but little relation to the actual strength of the 
masonry to be built. 

11. Quarry Examinations. These are generally the surest 
tests, and should never be neglected if the choice of stone is a matter 
of great importance. Field stone and outcropping rock which have 
withstood the weather for indefinite periods of years, can usually 
be relied on as being durable against all deterioration except that 
due to acids in the atmosphere, to w T hich they probably have not 
been subjected in the country as they might be in a city. On the other 
hand, however, large blocks of stone can seldom be obtained from 
field stones. If a quarry has been opened for several years, a com- 
parison of the other surfaces with those just exposed may indicate 
the possible disintegrating or discoloring effects of the atmosphere. 
A stone which is dense and of uniform structure, and which will not 
disintegrate, may be relied on to withstand any physical stress to 
which masonry should be subjected. 

BUILDING STONE 

12. Limestone. Carbonate of lime forms the principal in- 
gredient of limestone. A pure limestone should consist only of 
carbonate of lime. However, none of our natural stones are chemi- 
cally pure, but all contain a greater or less amount of foreign material. 
To these impurities are due the beautiful and variegated coloring 
which makes limestone valuable as a building material. 

Limestone occurs in stratified beds, and ordinarily is regarded 
as originating as a chemical deposit. It effervesces freely -when an 
acid is applied; its texture is destroyed by fire; the fire drives off its 
carbonic acid and water, and forms quicklime. Limestone varies 
greatly in its physical properties. Some limestones are very durable, 
hard, and strong, while others are very soft and easily broken. 

There are two principal classes of limestone — granular and 
compact. In each of these classes are found both marble and ordinary 
building stone. The granular stone is generally best for building 
purposes, and the finer-grained stones are usually better for either 
marble or fine cut-stone. The coarse-grained varieties often dis- 
integrate rapidly when exposed to the weather. All varieties work 
freely, and can be obtained in blocks of any desired dimensions. 

13. Marble. When limestone is wholly crystalline and suitable 



MASONRY AND REINFORCED CONCRETE 7 

for ornamental purposes, it is called marble; or, in other words, any 
limestone that can be polished is called marble. There are a great 
many varieties of marble, and they vary greatly in color and appear- 
ance. Owing to the cost of polishing marble, it is used chiefly for 
ornamental purposes. 

14. Dolomite. When the carbonate of magnesia occurring 
in limestone rises to about 45 per cent, the stone is then called dolo- 
mite. It is usually whitish or yellowish in color, and is a crystalline 
granular aggregate. It is harder than the ordinary limestones, and 
also less soluble, being scarcely at all acted upon by dilute hydrochloric 
acid. There is no essential difference between limestone and dolo- 
mite with respect to color and texture. 

15. Sandstone. Sandstones are composed of grains of sand 
that have been cemented together through the aid of heat and pres- 
sure, forming a solid rock. The cementing material usually is either 
silica, carbonate of lime, or an iron oxide. Upon the character of 
this cementing material is dependent, to a considerable extent, the 
color of the rock and its adaptability to architectural purposes. If 
silica alone is present, the rock is of a light color and frequently so 
hard that it can be worked only with great difficulty. Such stones 
are among the most durable of all rock, but their light color and poor 
working qualities are a drawback to their extensive use. Rocks in 
which carbonate of lime is the cementing material are frequently 
too soft, crumbling and disintegrating rapidly when exposed to the 
weather. For many reasons the rocks containing ferruginous cement 
(iron oxide) are preferable. They are neither too hard to work 
readily, nor liable to unfavorable alteration when exposed to at- 
mospheric agencies. These rocks usually have a brown or reddish 
color. 

Sandstones are of a great variety of colors, which, as has already 
been stated, is largely due to the iron contained in them. In texture, 
sandstones vary widely — from a stone of very fine grain, to one in 
which the individual grains are the size of a pea. Nearly all sand- 
stones are more or less porous, and hence permeable to a certain 
extent by water and moisture. Sandstones absorb water most 
readily in the direction of their lamination or grain. The strength 
and hardness of sandstones vary between wide limits. Most of the 
varieties are easily worked, and split evenly. The formations of 



8 MASONRY AND REINFORCED CONCRETE 

sandstone in the United States are very extensive. The crushing 
strength of sandstone varies widely, being from 2,500 pounds to 
13,500 pounds per square inch, and specimens have been obtained 
that require a load of 29,270 pounds per square inch to crush them. 

16. Conglomerates. Conglomerates differ from sandstone only 
in structure, being coarser and of a more uneven texture. The 
grains are usually an inch or more in diameter. 

17. Granite. The essential components of the true granites 
are quartz and potash feldspar. Granites are rendered complex, 
although the essential minerals are but two in number, by the presence 
of numerous accessories which essentially modify the appearance of 
the rocks; and these properties render them important as building 
stone. The prevailing color is some shade of gray, though greenish, 
yellowish, pink, and deep red are not uncommon. These various 
hues are due to the color of the prevailing feldspar and the amount 
and kind of the accessory minerals. The hardness of granite is due 
largely to the condition of the feldspathic constituent, which is valu- 
able. Granites of the same constituents differ in hardness. 

Granites do not effervesce with acids, but emit sparks when 
struck with steel. They possess the properties of strength, hardness, 
and durability, although they vary in these properties as well as in 
their structure. They furnish an extensive variety of the best stone 
for the various purposes of the engineer and architect. The crushing 
strength of granite is variable, but usually is between 15,000 and 
20,000 pounds per square inch. 

18. Trap Rock. Trap rock, or diabase, is a crystalline, granu- 
lar rock, composed essentially of feldspar and augite ; but nearly all 
contains magnetite and frequently olivine. They are basic in com- 
position and in structure; they are, as a rule, massive. The texture, 
as a general thing, is fine, compact, and homogeneous. The colors 
are somber, varying from greenish, through dark gray, to nearly 
black. Owing to its lack of rift, its hardness, and its compact tex- 
ture, trap rock is generally very hard to work. It has been used to 
some extent for building and monumental work, but is more generally 
used for paving purposes. Wthin the last few years, on account 
of its great strength and fire-resisting qualities, it has been extensively 
used in concrete work. The crushing strength of trap rock or dia- 
base is usually between 20,000 and 26,000 pounds per square inch. 




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MASONRY AND REINFORCED CONCRETE 9 

19. Seasoning of Stone. Stone, to weather well, should be 
laid with its bedding (lamination) horizontal, as it was first laid 
down by nature in the quarry. The stone, moreover, will offer 
greater resistance to pressure if laid in this manner, and, it is said, 
will stand a greater amount of heat without disintegrating. This 
is important in cities where any building is liable to have its walls 
highly heated by neighboring burning structures. 

Some stones that are liable to be destroyed by the effects of 
frost on first being taken from the quarries, are no longer so after 
being exposed for some time to the air, having lost their quarry 
water through evaporation. This difference is very manifest between 
stones quarried in summer and those quarried in winter. It has 
frequently happened that stones of good quality have been entirely 
ruined by hard freezing immediately after being taken from the 
quarry; while, if they are quarried during the warm season of the 
year and have an opportunity to lose their quarry water by evapora- 
tion prior to cold weather, they withstand freezing very well. This 
particularly applies to some marbles and limestones. This change is 
accounted for by the claim put forward, that the quarry water of the 
stones carries in solution carbonate of lime and silica, which is de- 
posited in the cavities of the rock as evaporation proceeds. Thus 
additional cementing material is added, rendering the rock more 
compact. This also will account for the hardening of some stones 
after being quarried a short time. When first quarried they are 
soft, easily sawed and worked into any desirable shape; but after the 
evaporation of their quarry water, they become hard and very durable. 

Table I gives the physical properties of many of the most im- 
portant varieties and grades of building stone found in the United 
States. 

BRICK 

20. Definition and Characteristics. The term brick is usually 
applied to the product resulting from burning moulded prisms of 
clay in a kiln at a high temperature. 

Common brick is not extensively used in engineering structures, 
except in the construction of sewers and the lining of tunnels. Brick 
is easily worked into structures of any desirable shape, easily handled 
or transported, and comparatively cheap. When well constructed, 



10 



MASONRY AND REINFORCED CONCRETE 



TABLE I 
Physical Properties of Building Stones 

(From Merrill's "Stone for Buildings and Decoration.") 



Kind of 
Stone 



Locality 





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Granite 

Granite 

Granite 
Granite 

Granite 
Diabase 
Limestone 
Limestone 

Limestone 
Limestone 
Limestone 
Limestone 
Sandstone 
Sandstone 

Sandstone 
Sandstone 

Sandstone 

Sandstone 

Sandstone 

Sandstone 



Grape Creek, Colo. 

Stony Creek, Conn. 

Milford, Conn. 
City Point, Me. 

East St. Cloud, Minn. 
New Duluth, Minn. 
Bedford, Ind. 

it it 

Greensburgh, Ind. 
Conshohocken, Pa. 
Stillwater, Minn. 

it a 

Buckhorn, Larimer Co., Colo. 

Fort Collins, Larimer Co. Colo. 

Brandford, Fremont Co., Colo. 
Marquette, Mich. 

Kasota, Minn. 

Albion, N. Y. 

Cleveland, O. 

Seneca, O. 



Bed 

Edge 

Bed 

Edge 



Bed 

Bed 

Edge 

Bed 

Edge 



j Bed 
i Edge 

\ Bed 
}Edge 

j Bed 
i Edge 
(Bed 
\Edge 

Bed 
Bed 
Bed 
Bed 
Bed 



(lbs.) 

14,492 

17,352 

15,000 
16,750 

22,610 

15,046 

28,000 
26,250 

26,250 
26,250 

6,500 

10,125 

16,875 

15,150 

25,000 

10,750 
12,750 

18,573 
17,261 

11,707 
10,784 

3,308 
2,894 

6,323 

10,700 

13,500 

6,800 

9,687 



2.603 
2.645 



2.65 
2.609 

3.005 



2.762 

2.567 

2.379 

2.252 

2.004 
2.166 

2.630 

2.420 

2.240 

2.390 



(lbs.) 
163 

165 



166 
163 

188 

147 

152 

170 



173 
161 
168 
141 

125 

135 

164 
151 
140 
149 



.048 

1 

201 



1 
338 

1 
24 

1 
32 

1 
117 



1 
251 

1 
40 

.040 
.072 



1 
^0~ 

1 
^6" 

1 
44 

1 
37 

1 
32 



MASONRY AND REINFORCED CONCRETE 11 

brick masonry compares very well in strength with stone masonry, 
but is not so heavy as stone. Brickwork is but slightly affected by 
changes of temperature or humidity. 

Brick is made of common clay (silicate of alumina), which 
usually contains compounds of lime, magnesia, and iron. Good 
brick clay is often found in a natural state. The quality of the brick 
depends greatly on the quality of the clay used, and equally as much 
on the care taken in its manufacture. 

Oxide of iron gives brick hardness and strength. The red color 
of brick is also due to the presence of iron. The presence of car- 
bonate of lime in the clay of which brick is made, is injurious, since 
the carbonate is decomposed during the burning, forming caustic 
potash, which, by the absorption of water, will cause the brick to 
disintegrate. An excess of silicate of lime makes the clay fusible, 
which softens the brick and thereby causes distortion during the 
burning process. Magnesia in small quantities has but little in- 
fluence on brick. Sand, in quantities not in excess of about 25 per 
cent, will help to preserve the form of the brick, and is beneficial 
to that extent; but in greater quantities than 25 per cent, it makes 
the brick brittle and weak. 

21. Requisites for Good Brick. Good brick should be of 
regular shape, with plane faces, parallel surfaces, and sharp edges and 
angles. It should show a fine, uniform, compact texture; should 
be hard, and, when struck a sharp blow, should ring clearly; and 
should not absorb more water than one-tenth of its weight. The 
specific gravity should be 2 or more. Good brick will bear a com- 
pressive load of 6,000 pounds per square inch when the sides are 
ground flat and pressed between plates. The modulus of rupture 
should be at least 800 pounds per square inch. 

22. Absorptive Power. The amount of water that a brick 
absorbs is very important in indicating the durability of brick, par- 
ticularly its resistance to frost. Very soft brick will absorb 25 to 
30 per cent of their weight of water. Weak, light-red ones will 
absorb 20 to 25 per cent; this grade of brick is used commonly for 
filling interior walls. The best brick will absorb only 4 to 5 per cent, 
but brick that will absorb 10 per cent is called good. 

23. Color of Bricks. The color of brick depends greatly 
upon the ingredients of the clay; but the temperature of the burn- 



12 MASONRY AND REINFORCED CONCRETE 

ing, the moulding sand, and the amount of air admitted to the kiln 
also have their influence. Pure clay or clay mixed with chalk will 
produce white brick. Iron oxide and pure clay will produce a bright 
red brick when burned at a moderate heat. Magnesia will produce 
brown brick; and when it is mixed with iron, produces yellow brick. 
Lime and iron in small quantities produce a cream color; an increase 
of lime produces brown, and an increase of iron red. 

24. Size and Weight. The standard size for common brick 
is 8 J by 4 by 2 J inches; and for face brick, 8f by 4 J by 2\ inches. There 
are numerous small variations from these figures; and also, since the 
shrinkage during burning is very considerable and not closely con- 
trolled, there is always some uncertainty and variation in the dimen- 
sions. Bricks will weigh from 100 to 150 pounds per cubic foot 
according to their density and hardness, the harder bricks being of 
course the heavier per unit of volume. 

25. Classification of Common Bricks. Bricks are usually 
classified in three ways: (a) Manner of moulding; (b) position in 
kiln; (c) their shape or use. 

(a) The manner in which brick is moulded has produced the 
following terms: 

Soft-mud Brick. A brick moulded either by hand or by machine, in 
which the clay is reduced to mud by adding water. 

Stiff-mud Brick. A brick moulded from dry or semi-dry clay. It is 
moulded by machinery. 

Pressed Brick. A brick moulded with semi-dry or dry clay. 

Re-pressed Brick. A brick made of soft mud, which, after being partly 
dried, is subjected to great pressure. * 

(b) The classification with regard to their position in the kiln 
applies only to the old method of burning. With the new methods., 
the quality is nearly uniform throughout the kiln. The three grades 
taken from the old-style kiln were: 

Arch Brick. Bricks forming the sides and top of the arches in which 
the fire is built are called arch bricks. They are hard, brittle, and weak 
from being over-burnt. 

Body, Cherry, or Hard Brick. Bricks from the interior are called body, 
cherry, or hard brick, and are of the best quality. 

Pale, Salmon, or Soft Brick. Bricks forming the exterior of the kiln 
are under-burnt, and are called soft, salmon, or pale brick. They are used 
only for filling, being too weak for ordinary use. 



MASONRY AND REINFORCED CONCRETE 



13 



(c) The classification of brick in regard to their use or shape 
has given rise to the following terms: 

Face Brick. Brick that are uniform in size and color and are suitable 
for the exposed places of buildings. 

Sewer Brick. Common hard brick, smooth and regular in form. 

Paving Brick. Very hard common vitrified brick, often made of shale. 
They are larger than the ordinary brick, and are often called paving blocks. 

Compass Brick. Brick having four short edges which run radially to 
an axis. They are used to build circular chimneys. 

Voussoir Brick. Brick having four long edges running radially to an 
axis. They-are used in building arches. 

2G. Crushing Strength. The results of crushing tests of brick 
vary greatly, depending on the details of the tests made. Many 
reports fail to give the details under which these tests are made, and 
in that case the real value of the results of the test as announced is 
greatly reduced. 

The following results were obtained at the U. S. Arsenal at 
Watertown, Mass., by F. E. Kidder. The specimens were rubbed 
on a revolving bed until the top and bottom faces were perfectly true 
and parallel. 



Make of'Brick 


No. of Specimens 
Tested 


Pressure at 

which Specimens 

Began to Fail 


Compression 
(per sq. in.) 


Philadelphia Face Brick 
Cambridge Brick 
Boston Brick 
New England Pressed 


3 
4 
3 
4 


3,-527 ibs. 
4,655 " 
7,880 " 
4,764 " 


5,918 lbs. 
12, 186 " 
11,670 " 
12,490 " 



The following results were obtained by C. Y. Davis, the tests 
being made at the Watertown Arsenal: 



Kind of 


Compression 


Kind of 


Compression 


Kind op 


Compression 


Brick 


(per sq. in.) 


Brick 


(per sq.in.) 


Brick 


(per sq. in.) 


Red 


' 9,540 lbs. 


Pressed 


6,470 lbs. 


Arch 


7,600 lbs. 


" 


*8,530 " 


" 


*9,190 " 


" 


♦10,290 " 


it 


6,050 " 


it 


5,960 " 


a 


6,800 " 


" 


6,700 " 


<> 


6,750 " 







These specimens were tested to select brick for the U.S. Pension Office at Wash- 
ington. D. C The specimens tested were submitted by manufacturers. 
♦Indicates the brick selected. 

27. Fire Brick. Furnaces must be lined with a material which 



14 MASONRY AND REINFORCED CONCRETE 



is even more refractory than ordinary brick. The oxide and sulphide 
of iron, which are so common (and comparatively harmless) in ordinary 
brick, will ruin a fire brick if they are present to a greater extent than 
a very few per cent. Fire brick should be made from nearly pure 
sand and clay. There is comparatively little need for mechanical 
strength, but the chief requirement is their infusibility, and pure 
clay and silica fulfil this requirement very perfectly. 

28. Sand=Lime Brick. Within the last few years, the sand- 
lime brick industry has been developed to some extent. The ma- 
terials for making this brick consist of sand and lime ; and they were 
first made by moulding ordinary lime mortar in the shape of a clay 
brick, and were hardened by the carbon dioxide of the atmosphere. 

There are two general methods of manufacturing these bricks: 

(a) Brick made of sand and lime, and hardened in the atmosphere. 
This hardening may be hastened by placing the brick in an atmosphere rich 
in carbon dioxide; or still less time will be required if the hardening is done 
with carbon dioxide under pressure. 

(6) Brick made of sand and lime, and hardened by steam under 
atmospheric pressure. This process may be hastened by having the steam 
under pressure. 

When sand-lime bricks are made by the first process, it requires 
several weeks for the bricks to harden; and by the second method 
it requires only a few hours; the latter method is the one generally 
used in this country. The advantages claimed for these bricks are 
that they improve with age; are more uniform in size, shape, and 
color; have a low porosity and no efflorescence; and do not disin- 
tegrate by freezing. The compressive strength of sand-lime brick 
of a good quality ranges from 2,500 to 4,500 pounds per square inch. 

CONCRETE BUILDING BLOCKS 

29. The growth of the concrete block industry has been rapid. 
The blocks are taking the place of wood, brick, and stone for ordi- 
nary wall construction. They are strong, durable, and cheap. The 
blocks are made at a factory or on the site of the work where they 
are to be used, and are placed in the wall in the same manner as 
brick or stone. There are two general types of blocks made — the 
one-piece block, and the two-piece block. The one-piece type consists 
of a single block, with hollow cores, making the whole thickness of 
the wall. In the two-piece type, the front and back of the blocks are 



MASONRY AND REINFORCED CONCRETE 15 

made in two separate pieces, and bonded when laid up in the wall. 
The one-piece blocks are more generally used than the two-piece 
blocks. 

30. Size of BlockSc Various shapes and sizes of blocks are 
made. Builders of some of the standard machines have adopted a 
standard length of 32 inches and a height of 9 inches for the full- 
sized blocks, with width of 8, 10, and 12 inches. Lengths of S, 12, 16, 
20, and 24 inches are made from the same machine, by the use of 
parting plates and suitably divided face-plates. Most machines 
are constructed so that any length between 4 and 32 inches, and any 
desired height, can be obtained. 

The size of the openings (the cores) varies from one-third 
to one-half of the surface of the top or bottom of the block. The 
building laws of many cities state that the openings shall amount to 
only one-third of the surface. For any ordinary purpose, blocks 
with 50 per cent open space are stronger than necessary. 

31. Material. The material for making concrete blocks con- 
sists of Portland cement, sand, and crushed stone or gravel. Owing 
to the narrow space to be filled with concrete, the stone and gravel 
are limited to one-half or three-quarters of an inch in size. At least 
one-third of the material, by weight, should be coarser than £ 
inch. A block made with gravel or screenings (sand to f-inch stone), 
with proportions of 1 part Portland cement to 5 parts screenings, will 
be as good as a block with 1 part Portland cement and 3 parts sand. 
These materials will be further treated under the headings of 'Tort- 
land Cement," "Sand," and "Stone." 

32. Proportions. The proportions generally used in the 
making of concrete blocks, vary from a mixture of 1 part cement, 
2 parts sand, and 4 parts stone, to a mixture of 1 part cement, 3 parts 
sand, and 6 parts stone. A very common mixture consists of 1 part 
cement, 2k parts sand, and 5 parts stone. A denser mixture may 
be secured by varying these proportions somewhat; that is, the maker 
may find that he secures a more compact block by using 2f parts 
sand and 4f parts stone; but a leaner mixture than 1 : 2 } : 5 is not 
to be recommended. In strength this mixture will have a crushing 
resistance far beyond any load that it will ever have to support. Even 
a mixture of 1:3:6 or 1:3}: 7 will be stronger than necessary 
to sustain any ordinary load. Such a mixture, however, would be 



16 MASONRY AND REINFORCED CONCRETE 



porous and unsatisfactory in the wall of a building. Blocks, in being 
handled at the factory, carted to the building site, and in being 
placed in the wall, will necessarily receive more or less rough handling; 
and safety in this respect calls for a stronger block than is needed to 
bear the weight of a wall of a building. For a high-grade water-tight 
block, a 1 : 2 : 4 or a 1 : 2 J : 4 mixture is generally used. 

33. Proportion of Water. Blocks made with dry concrete 
will be soft and weak, even if they are well sprinkled after being taken 
out of the forms. Blocks that are to be removed from the machine 
as soon as they are made will stick to the plates and sag out of shape, 
if the concrete is mixed too wet. Therefore there should be as much 
water as possible used, without causing the block to stick or sag out 
of shape when being removed from the moulds. This amount of 
water is generally 8 to 9 per cent of the weight of the dry mixture. 
To secure uniform blocks in strength and color, the same amount 
of water should be used for each batch. 

34. Mixing and Tamping. The concrete should be mixed in a 
batch mixer, although good results are obtained in hand-mixed con- 
crete. The tamping is generally done with hand-rammers. Pneu- 
matic tampers, operated by an air-compressor, are used successfully. 
Moulding concrete by pressure is not successful unless the concrete 
is laid in comparatively thin layers. 

35. Curing of Blocks. The blocks are removed from the 
machine on a steel plate, on which they should remain for 24 hours. 
The blocks should be protected from the sun and dry winds for at 
least a week, and thoroughly sprinkled frequently. They should be 
at least four weeks old before they are placed in a wall. If they 
are built up in a wall while green, skrinkage cracks will be apt to 
occur in the joints. 

36. Mixture for Facing. For appearance, a facing of a richer 
mixture is often used, generally consisting of 1 part cement to 2 parts 
sand. The penetration of water may be effectively prevented by this 
rich coat. Care must be taken to avoid a seam between the two 
mixtures. 

Blocks are made with either a plane face, or of various orna- 
mental patterns, as tool-faced, paneled, rock-faced, etc. Coloring 
of the face is often desired. Mineral coloring, rather than chemical, 
should be used, as the chemical color may injure the concrete or fade. 



MASONRY AND REINFORCED CONCRETE 17 

37. Cost of Making. The following is quoted from a paper by 
N. F. Palmer, C. E.: 

Blocks 8 by 9 by 32 inches; gang consisted of five workmen, and 
foreman; record for one hour, 30 blocks; general average for 10 hours, 200 
blocks. The itemized cost was as follows: 

1 foreman @ $2 . 50 $ 2 . 50 

5 helpers @ 2.00 10.00 

13 bbls. cement @ 2.00 26.00 

10 cu. yds. sand and gravel @ 1 . 00 10 . 00 

Interest and depreciation on machine 2 . 00 

$50 . 50 
This is the equivalent of $50.50 -4- 200, or 25\ cents per block; or, 
since the face of the block was 9 by 32 inches, or exactly 2 square feet, the 
equivalent of 12.6 cents per square foot of an 8-inch wall. 

Another illustration, quoted from Gillette, for a 10-inch wall, 
was itemized as follows, for each square foot of wall : 

Sand 2.0 cents 

Cement @ $1.60 per barrel 4.5 " 

Labor @ $1 . 83 per day 3.8 " 

Total per square foot 10.3 " 

This is apparently considerably cheaper than the first case, even after 
allowing for the fact that the second case does not provide for interest, depre- 
ciation on plant, etc., which in the first case is only 4 per cent of the total. 
This allowance of 4 per cent is probably too small. 

CEMENTING MATERIALS 

38. The principal cementing materials are Common Lime, 
Hydraulic Lime, Pozzuolana, Natural Cement, and Portland Cement. 
There are a few other varieties, but their use is so limited that they 
need not be considered here. 

39. Common Lime. This is produced by burning "limestone" 
whose chief ingredient is carbonate of lime. Except in the form of 
marble, a limestone usually contains other substances — perhaps up 
to 10 per cent of silica, alumina, magnesia, etc. The process of 
burning drives off the carbonic acid, and leaves the protoxide of 
calcium. This is the lime of commerce; and to preserve it from 
deterioration, it must be kept dry and even protected from a free 
circulation of air. When exposed freely to the air for a long period, 
it will become air-slaked; that is, it will absorb both moisture and 
carbonic acid from the air, and will lose it° ability to harden. The 



18 MASONRY AND REINFORCED CONCRETE 

first step in using common lime is to combine it with water, which 
it absorbs readily so that its volume is increased to 2\ or Z\ times 
what it was before. Its weight is at the same time increased about 
one-fourth; and the mass, which consisted originally of large lumps 
with some powder, is reduced to an unctuous mass of smooth paste. 
The lime tt is then called slaked lime, the process of slaking being 
accompanied by the development of great heat. The purer the lime, 
the greater the development of heat and the" greater the expansion 
in volume. It is soluble in water which is not already "hard," or 
which does not already contain considerable lime in solution. A 
good lime will make a smooth paste with only a very small per- 
centage (less than 10 per cent) of foreign matter or clinker. By 
such simple means a lime may be readily tested. 

The hardening of common lime mortar is due to the formation 
of a carbonate of lime (substantially the original condition of the 
stone) by the absorption from the atmosphere of carbonic oxide. 
This will penetrate for a considerable depth in course of time; but 
instances are common in which masonry has been torn down after 
having been erected many years, and the lime mortar in the interior 
of the mass has been found still soft and unset, since it was hermeti- 
cally cut off from the carbonic oxide of the atmosphere. For the 
same reason, common lime mortar will not harden underwater, and 
therefore it is utterly useless to employ it for work under water or 
for large masses of masonry. 

When the qualities of slaking and expansion are not realized or 
are obtained only very imperfectly, the lime is called lean or poor 
(rather than fat) x&nd its value is less and less, until it is perhaps 
worthless for use in making mortar, or for any other use except as 
fertilizer. The cost of lime is about 60 cents per barrel of 230 pounds 
net. 

40. Hydraulic Lime. This is derived from limestones con- 
taining about 10 to 20 per-cent of clay or silica, which is intimately 
mixed with the carbonate of lime in the structure of the stone. Dur- 
ing the process of burning, some of the lime combines with the clay 
(or the silica) so as to form the aluminate or silicate of lime. The 
excess of lime becomes quicklime as before. During the process of 
slaking, which should be done by mere sprinkling, the lime having 
been intimately mixed with the clay or silica, the expansion of the 



MASONRY AND REINFORCED CONCRETE 19 

lime completely disintegrates the whole mass. This slaking is done 
by the manufacturer. The lime having a much greater avidity for 
the water than the aluminate or the silicate, the small amount of 
water used in the slaking is absorbed entirely by the lime, and the 
aluminate or the silicate is not affected. The setting of hydraulic 
lime appears to be due to the crystallizing of the aluminate 
and silicate; and since this will be accomplished even when the 
masonry is under water, it receives from this property its name of 
hydraulic lime. It is used but little in this country, and is all im- 
ported. 

41. Pozzuolana or Slag Cement. Pozzuolana is a form of 
cementing material which has been somewhat in use since very 
ancient times. Apparently it was first made from the lava from the 
volcano Vesuvius, the lava being picked up at Pozzuoli, a village near 
the base of the volcano. It consists of a combination of silica and 
alumina, which is mixed with common lime. Its chemical composi- 
tion is therefore not very unlike that of hydraulic lime. It also 
possesses the ability to harden under water. Its use is very limited, 
and its strength and hardness comparatively small, compared with 
that of Portland cement. It should never be used where it will be 
exposed for a long time to dry air, even after it has thoroughly set. 
It appears to withstand the action of sea water somewhat better than 
Portland cement; and hence it is sometimes used instead of Portland 
cement as the cementing material for large masses of masonry or 
concrete which are to be deposited in sea water, when the strength 
of the cement is a comparatively minor consideration. Artificial 
pozzuolana is sometimes made by grinding up blast-furnace slag 
which has been found by chemical analysis to have the correct chemi- 
cal composition. 

42. Natural Cement. Natural cement is obtained by burning 
an argillaceous or a magnesian limestone which happens to have 
the proper chemical composition. The resulting clinker is then 
finely ground and is at once ready for use. Such cement was 
formerly and is still commonly called Rosendale cement, owing 
to its having been produced first in Rosendale, Ulster County, 
New York. A very large part of the natural cement now pro- 
duced in this country comes from Ulster County, New York, 
or from near Louisville, Kentucky. Cement rock from which 



20 MASONRY AND REINFORCED CONCRETE 

natural cement can be made, is now found widely scattered over 
the country. 

In Europe the name Roman cement is applied to substantially 
the same kind of product. Since the cement is made wholly from 
the rock just as it is taken out of the quarry, and also since it is cal- 
cined at a much lower temperature than that employed in making 
Portland cement, it is considerably cheaper than Portland cement. 
On the other hand, its strength is considerably less than that of 
Portland cement, and the time of setting is much quicker. Some- 
times this quickness of setting is a very important point — as, for 
instance, when it is desired to obtain a concrete which shall attain 
considerable hardness very quickly. On the other hand, the quick- 
ness of setting may be a serious disadvantage, because it may not 
allow sufficient time to finish the concrete work satisfactorily and 
prevent the disturbance of mortar which has already taken an initial 
set. Natural cement is still largely used, on account of its cheapness, 
especially when the cement is not required to have very great strength. 
The disadvantage due to its quick setting (when it is a disadvantage) 
may be somewhat overcome by the use of a small percentage of lime 
when mixing up the mortar. 

It is not always admitted, at least in the advertisements, that a 
given brand of cement is a natural cement; and the engineer must 
therefore be on his guard, in buying a cement, to know whether it is 
a quick-setting natural cement of comparatively low strength or a 
true Portland cement. 

43. Portland Cement. Portland cement consists of the prod- 
uct of burning and grinding an artificial mixture of carbonate of 
lime and clay or slag, the mixture being very carefully proportioned 
so that the ingredients shall have very nearly the fixed ratio which 
experience has demonstrated to give the best results. 

"If a deposit of stone containing exactly the right amount of clay, and 
of exactly uniform composition, could be found, Portland cement could be 
made from it, simply by burning and grinding. For good results, however, 
the composition of the raw material must be exact, and the proportion of 
carbonate of lime in it must not vary even by one per cent. No natural 
deposit of rock of exactly this correct and unvarying composition is known 
or likely ever to be found; therefore Portland cement is always made from 
an artificial mixture, usually, if free from organic matter, containing about 
75 per cent carbonate of lime and 25 per cent clay." — S. B. Newberry, in 
Taylor and Thompson's "Concrete Plain and Reinforced." 




REINFORCED-CCNCRETE COAL POCKET AT CONCORD, VIRGINIA 

Designed by Webb & Gibson, Philadelphia, Pa. 



MASONRY AND REINFORCED CONCRETE 21 

As before stated, Portland cement is stronger than natural 
cement; it sets more slowly, which is frequently a matter of great 
advantage, and yet its rate of setting is seldom so slow that it is a 
disadvantage. Although the cost is usually greater than that of 
natural cement, yet improved methods of manufacture have re- 
duced its cost so that it is now usually employed for all high- 
grade work where high ultimate strength is an important consid- 
eration. 

In a general way, it may be said that the characteristics of 
Portland cement on which its value as a material to be used in con- 
struction work chiefly depends may be briefly indicated as follows : 

When the cement is mixed with water and allowed to set, it 
should harden in a few hours, and should develop a considerable 
proportion of its ultimate strength in a few days. It should also 
possess the quality of permanency so that no material change in 
form or volume will take place on account of its inherent quali- 
ties or as the result of exterior agencies. There is always found 
to be more or less of shrinkage in the volume of cement and con- 
crete during the process of setting and hardening; but with any 
cement of really good quality, this shrinkage is not so great as to 
prove objectionable. Another very important characteristic is that 
the cement shall not lose its strength with age. Although some 
long-time tests of cement have apparently indicated a slight de- 
crease in the strength of cement after the first year or so, this 
decrease is nevertheless so slight that it need not affect the design 
of concrete, even assuming the accuracy of the general statement. 

To insure absolute dependence on the strength and durability 
of any cement which it is proposed to use in important structural 
work, it is essential that the qualities of the cement be deter- 
mined by thorough tests. 

CEMENT TESTING 

44. The thorough testing of cement, as it is done for the largest 
public works, should properly be done in a professional testing 
laboratory. A textbook of several hundred pages has recently been 
written on this subject. The ultimate analysis and testing of cement, 
both chemically and physically, is beyond the province of the ordinary 
engineer. But the ordinary engineer does have frequent occasion 



22 MASONRY AND REINFORCED CONCRETE 

to obtain cement in small quantities when testing in professional 
laboratories is inconvenient or unduly expensive. Fortunately it 
is possible to make some simple tests without elaborate apparatus 
which will at least show whether the cement is radically defective 
and unfit for use. It is unfortunately true that an occasional barrel 
of even the best brand of cement will prove to be very inferior to the 
standard output of that brand. This practically means that in any 
important work, using a large quantity of cement, it is not sufficient 
to choose a brand, as the result of preliminary favorable tests, and 
then accept all shipments without further test. Several barrels in 
every carload should be sampled for testing. It is not too much to 
prescribe that every barrel should be tested by at least a few of the 
simpler forms of testing given below. The following methods of 
testing are condensed from the progress report of the Committee on 
Uniform Tests of Cement, as selected by the American Society of 
Civil Engineers. The statements may therefore be considered as 
having the highest authority obtainable on this subject. 

45. Sampling. The number of samples that should be taken 
depends on the importance of the work but it is chiefly important 
that the sample should represent a fair average of the contents. The 
sample should be passed through a sieve having twenty meshes per 
linear inch, in order to break up lumps and remove any foreign 
material. If several small amounts are taken from different 
parts of the package, this also insures that the samples will be mixed 
so that the result will be a fair average. When it is only desired to 
determine the average characteristic of a shipment, the samples taken 
from different parts of the shipment may be mixed, but it will give 
a better idea of the uniformity of the product to analyze the dif- 
ferent samples separately. Cement should be taken from a barrel 
by boring a hole. through the center of one of the staves, midway 
between the heads, or through the head. A portion of the cement can 
then be withdrawn, even from the center, by means of a sampling iron 
similar to that used by sugar inspectors. 

46. Chemical Analysis. Ordinarily, it is impracticable for an 
engineer to make a chemical analysis of cement which will furnish 
reliable information regarding its desirability, but the engineer 
should understand something regarding the desirable chemical 
constituents of the cement. It should be realized that the fineness 



MASONRY AND REINFORCED CONCRETE 23 

of the grinding and the thoroughness of the burning may have a far 
greater influence on the value of the cement than slight variations 
from the recognized standard proportions of the various chemical 
constituents. Too high a proportion of lime will cause failure in 
the test for soundness or constancy of volume, although a cement 
may fail on such a test owing to improper preparation of the raw 
material or defective burning. On the other hand, if the cement 
is made from very finely ground material and is thoroughly burned, 
it may contain a considerable excess of lime and still prove perfectly 
sound. The permissible amount of magnesia in Portland cement 
is the subject of considerable controversy. Some authorities say 
that anything in excess of 8 per cent is harmful, others declare that 
the amount should not exceed 4 per cent or 5 per cent. The pro- 
portion of sulphuric-anhydride should not exceed 1.75 per cent. It 
may be considered that the other tests of cement are a far more reli- 
able indication of its quality than any small variation in the chemical 
constituents from the proportions usually considered standard. 

47. Specific Gravity. The specific gravity of cement is lowered 
by under-burning, adulteration, and hydration, but the adulteration 
must be in considerable quantities to affect the results. Since the dif- 
ferences in specific gravity are usually very small, great care must be 
exercised in making the tests. When properly made, the tests afford 
a quick check for under-burning or adulteration. The determination 
of specific gravity is conveniently made with Le Chatelier's apparatus. 
This consists of a flask D, Fig. 1, of 120-cu. cm. (7.32-cu. in.) capac- 
ity, the neck of which is about 20 cm. (7.87 in.) long; in the middle 
of this neck is a ball C, above and below which are two marks F and 
E; the volume between these marks is 20 cu. cm. (1.22 cu. in.). The 
neck has a diameter of about 9 mm. (0.35 in.), and is graduated into 
tenths of cu. cm. above the mark F. Benzine (62° Baume naphtha), 
or kerosene free from water, should be used in making the determina- 
tion. 

The specific gravity may be determined in two ways: 

First. The flask is filled with either of these liquids to the lower 

mark E, and 64 gr. (2.25 oz.) of powder, previously dried at 100° 

Cent. (212° Fahr.) and cooled to the temperature of the liquid, is 

gradually introduced through the funnel B (the stem of which extends 



24 



MASONRY AND REINFORCED CONCRETE 



into the flask to the top of the bulb C) until the proper mark F is 
reached. The difference in weight between the cement remaining 
and the original quantity (64 gr.) is the weight which has displaced 
20 cu. cm. 

Second. The whole quantity of powder is introduced, and the 





Fig. 1. Le Chatelier's Apparatus for Determining Specific Gravity. 

level of the liquid rises to some division of the graduated neck. This 
reading plus 20 cu. cm. is the volume displaced by 64 gr. of the powder. 
The specific gravity is then obtained from the formula: 



Specific Gravity 



Weight of cement 
Displaced volume 



The flask during the operation is kept in water in a jar A in 
order to avoid variation in [the temperature of the liquid. The 
results should agree within 0.01. 

48. Fineness. It is generally accepted that the coarser mate- 
rials in cement are practically inert, and it is only the extremely fine 
powder that possesses adhesive cementing qualities. The more finely 



MASONRY AND REINFORCED CONCRETE 25 

cement is pulverized, all other conditions being the same, the more 
sand it will carry and produce a mortar of a given strength. The de- 
gree of pulverization which the cement receives at the place of manu- 
facture is ascertained by measuring the residue retained on certain 
sieves. Those known as No. 100 and- No. 200 sieves are recommended 
for this purpose. The sieve should be circular, about 20 cm. (7.87 
inches) in diameter, 6 cm. (2.36 inches) high, and provided with 
a pan 5 cm. (1.97 inches) deep, and a cover. The wire cloth should 
be woven from brass wire having the following diameters: No. 100, 
0.0045 inches; No. 200, 0.0024 inches. This cloth should be mounted 
on the frame without distortion. The mesh should be regular in 
spacing and be within the following limits: 



No. 100, 96 to 100 meshes to the linear inch. 
No. 200, 188 to 200 meshes to the linear inch. 



50 grams (1.76 oz.) or 100 gr. (3.52 oz.) should be used for the test 
and dried at a temperature of 100° Cent, or 212° Fahr., prior to 
sieving. 

The thoroughly dried and coarsely screened sample is weighed 
and placed on the No. 200 sieve, which, with pan and cover attached, 
is held in one hand in a slightly inclined position, and moved forward 
and backward, at the same time striking the side gently with the palm 
of the other hand, at the rate of about 200 strokes per minute. The 
operation is continued until not more than ^ of 1 per cent passes 
through after one minute of continuous sieving. The residue is 
weighed, then placed on the No. 100 sieve and the operation repeated. 
The work may be expedited by placing in the sieve a small quantity of 
large shot. The results should be reported to the nearest tenth of 
1 per cent. 

49. Normal Consistency. The use of a proper percentage of 
water in making the pastes, cement and water, from which pats, tests 
of setting, and briquettes are made, is exceedingly important, and af- 
fects vitally the results obtained. The determination consists in meas- 
uring the amount of water required to reduce the cement to a given 
state of plasticity, or to what is usually designated the normal consist- 



26 



MASONRY AND REINFORCED CONCRETE 



ency. Various methods have been proposed for making this deter- 
mination, none of which has been found entirely satisfactory. The 
Committee recommends the following: 

The apparatus for this test consists of a frame K, Fig. 2, bearing 
a movable rod L, with the cap A at one end, and at the other the 
cylinder B, 1 cm. (0.39 in.) in diameter, the cap, rod, and cylinder 
weighing 300 gr. (10.58 oz.). The rod, which can be held in any 




Fig. 2. Apparatus for Testing Normal Consistency of Cement. 



desired position by a screw F, carries an indicator, which moves 
over a scale (graduated to centimeters) attached to the frame K. 
The paste is held by a conical, hard-rubber ring I, 7 cm. (2.76 in.) 
in diameter at the base, 4 cm. (1.57 in.) high, resting on a glass 
plate J about 10 cm. (3.94 in. square). 

In making the determination, the same quantity of cement as 
will be subsequently used for each batch in making the briquettes 
(but not less than 500 grams) is kneaded into a paste, as described 
later in paragraph on "Mixing," and quickly formed into a ball with 
the hands, completing the operation by tossing it six limes from one 
hand to the other, maintained 6 inches apart; the ball is then pressed 



MASONRY AND REINFORCED CONCRETE 



27 



into the rubber ring, through the larger opening, smoothed off, and 
placed (on its large end) on a glass plate and the smaller end smoothed 
off with a trowel ; the paste confined in the ring, resting on the plate, 
is placed under the rod bearing the cylinder, which is brought in 
contact with the surface and quickly released. 

The paste is of normal consistency when the cylinder penetrates 
to a point in the mass 10 mm. (0.39 in.) below the top of the ring. 
Great care must be taken to fill the ring exactly to the top. The 
trial pastes are made with varying percentages of water until the cor- 
rect consistency is obtained. The Committee has recommended, as 
normal, a paste the consistency of which is rather wet, because it 
believes that variations in the amount of compression to which the 
briquette is subjected in moulding are likely to be less with such a 
paste. Having determined in this manner the proper percentage 
of water required to produce a paste of normal consistency, the proper 
percentage required for the mortars is obtained from an empirical 
formula. The Committee hopes to devise a formula. The sub- 
ject proves to be a very difficult one, and, although the Committee 
has given it much study, it is not yet prepared to make a definite 
recommendation. 

Note. The Committee on Standard Specifications for Cement 
inserts the following table for temporary use to be replaced by one 
to be devised by the Committee of the American Society of Civil 

Engineers. 

TABLE II 
Percentage of Water for Standard Sand Mortars 



Percentage 


One Cement 


Percentage 


One Cement 


Percentage 


One Cement 


of Water 


Three 


of Water 


Three 


of Water 


Three 


for 


Standard 


for 


Standard 


for 


Standard 


Neat Cement 


Ottawa Sand 


Neat Cement 


Ottawa Sand 


Neat Cement 


Ottawa Sand 


15 


8.0 


23 


9.3 


31 


10.7 


16 


8.2 


24 


9.5 


32 


10.8 


17 


8.3 


25 


9.7 


33 


11.0 


18 


8.5 


26 


9.8 


34 


11.2 


19 


8.7 


27 


10.0 


35 


11.5 


20 


8.8 


28 


10.2 


36 


11.5 


21 


9.0 


29 


10.3 


37 


11.7 


22 


9.2 


30 


10.5 


38 


11.8 




1 to 1 


1 to 2 


1 to 3 


1 to 4 


1 to 5 


Cement. . . 


500 


333 


250 


200 


167 


Sand 


500 


666 


750 


800 


833 



50. Time of Setting. The object of this test is to determine the 
time which elapsed from the moment water is added until the paste 



28 MASONRY AND REINFORCED CONCRETE 



ceases to be fluid and plastic (called the "initial set"), and also the 
time required for it to acquire a certain degree of hardness (called 
the "final" or "hard set"). The former of these is the more important, 
since, with the commencement of setting, the process of crystalliza- 
tion or hardening is said to begin. As a disturbance of this process 
may produce a loss of strength, it is desirable to complete the opera- 
tion of mixing and moulding or incorporating the mortar into the 
work before the cement begins to set. It is usual to measure arbi- 
trarily the beginning and end of the setting by the penetration of 
weighted wires of given diameters. 

For this purpose the Vicat Needle, which has already been de- 
scribed, should be used. In making the test, a paste of normal consist- 
ency is moulded and placed under the rod L, Fig. 2, as described in a 
previous paragraph. This rod bears the cap D at one end and the 
needle H, 1 mm. (0.039 in.) in diameter, at the other, and weighs 
300 gr. (10.58 oz.). The needle is then carefully brought in contact 
with the surface of the paste and quickly released. The setting is 
said to have commenced when the needle ceases to pass a point 5 mm. 
(0.20 in.) above the upper surface of the glass plate, and is said to 
have terminated the moment the needle does not sink visibly into 
the mass. 

The test pieces should be stored in moist air during the 
test; this is accomplished by placing them on a rack over water con- 
tained in a pan and covered with a damp cloth, the cloth to be kept 
away from them by means of a wire screen ; or they may be stored 
in a moist box or closet. Care should be taken to keep the needle 
clean, as the collection of cement on the sides of the needle retards 
the penetration, while cement on the point reduces the area and 
tends to increase the penetration. The determination of the time of 
setting is only approximate, being materially affected by the tem- 
perature of the mixing water, the temperature and humidity of the 
air during the test, the percentage of water used, and the amount 
of moulding the paste receives. 

The following approximate method, not requiring the use of 
apparatus, is sometimes used, although not referred to by the Com- 
mittee. Spread cement paste of the proper consistency on a piece 
of glass, having the cement cake about three inches in diameter and 
about one inch thick at the center, thinning towards the edges. When 



MASONRY AND REINFORCED CONCRETE 



29 



the cake is hard enough to bear a gentle pressure of the finger nail, 
the cement has begun to set, and when it is not indented by a con- 
siderable pressure of the thumb nail, it is said to have set. 

51. Standard Sand. The Committee recognizes the grave objec- 
tions to the standard quartz now generally used, especially on account 
of its high percentage of voids, the difficulty of compacting in the 
moulds, and its lack of uniformity; it has spent much time in investi- 




Fig. 3. Form of Briquette. 



gating the various natural sands which appeared to be available and 
suitable for use. For the present, the Committee recommends the 
natural sand from Ottawa, 111., screened to pass a sieve having 20 
meshes per linear inch and retained on a sieve having 30 meshes per 
linear inch; the wires to have diameters of 0.0165 and 0.0112 inches, 
respectively, i.e., half the width of the opening in each case. Sand 
having passed the No. 20 sieve shall be considered standard when 



30 MASONRY AND REINFORCED CONCRETE 

not more than one per cent passes a No. 30 sieve after one minute 
continuous sifting of a 500-gram sample. 

52. Form of Briquette. While the form of the briquette recom- 
mended by a former Committee of the Society is not wholly satis- 
factory, this Committee is not prepared to suggest any change, other 
than rounding off the corners by curves of J-inch radius, Fig. 3. 

53. Moulds. The moulds should be made of brass, bronze, or 
some equally non-corrodible material, having sufficient metal in the 
sides to prevent spreading during moulding. 

Gang moulds, which permit moulding a number of briquettes 
at one time, are preferred by many to single moulds; since the greater 






A 



Fig. 4. Gang Moulds. 

quantity of mortar that can be mixed tends to produce greater uni- 
formity in the results. The type shown in Fig. 4 is recommended. 
The moulds should be wiped with an oily cloth before using. 

54. Mixing. All proportions should be stated by weight; the 
quantity of water to be used should be stated as a percentage of the 
dry material. The metric system is recommended because of the con- 
venient relation of the gram and the cubic centimeter. The tem- 
perature of the room and the mixing water should be as near 21° 
Cent. (70° Fahr.) as it is practicable to maintain it. The sand and 
cement should be thoroughly mixed dry. The mixing should be 
done on some non-absorbing surface, preferably plate glass. If the 
mixing must be done on an absorbing surface it should be thoroughly 
dampened prior to use. The quantity of material to be mixed at 
one time depends on the number of test pieces to be made; about 
1000 gr. (35.28 oz.) makes a convenient quantity to mix, especially 
by hand methods. 

The material is weighed and placed on the mixing table, and a 
crater formed in the center, into which the proper percentage of 
clean water is poured ; the material on the outer edge is turned into the 
crater by the aid of a trowel. As soon as the water has been absorbed, 



MASONRY AND REINFORCED CONCRETE 31 

which should not require more than one minute, the operation is 
completed by vigorously kneading with the hands for an additional 
1 J minutes, the process being similar to that used in kneading dough. 
A sand-glass affords a convenient guide for the time of kneading. 
During the operation of mixing the hands should be protected by 
gloves, preferably of rubber. 

55. Moulding. Having worked the paste or mortar to the 
proper consistency, it is at once placed in the moulds by hand. The 
moulds should be filled at once, the material pressed in firmly with the 
fingers and smoothed off with a trowel without ramming; the material 
should be heaped up on the upper surface of the mould, and, in 
smoothing off, the trowel should be drawn over the mould in such a 
manner as to exert a moderate pressure on the excess material. The 
mould should be turned over and the operation repeated. A check 
upon the uniformity of the mixing and moulding is afforded by weigh- 
ing the briquettes just prior to immersion, or upon removal from the 
moist closet. Briquettes wdiich vary in weight more than 3 per cent 
from the average should not be tested. 

56. Storage of the Test Pieces. During the first 24 hours after 
moulding, the test pieces should be kept in moist air to prevent them 
from drying out. A moist closet or chamber is so easily devised that 
the use of the damp cloth should be abandoned if possible. Covering 
the test pieces with a damp cloth is objectionable, as commonly used, 
because the cloth may dry out unequally, and, in consequence, the 
test pieces are not all maintained under the same condition. Where 
a moist closet is not available, a cloth may be used and kept uni- 
formly wet by immersing the ends in water. It should be kept from 
direct contact with the test pieces by means of a wire screen or some 
similar arrangement. 

A moist closet consists of a soapstone or slate box, or a metal- 
lined wooden box: the metal lining being covered with felt and this 
felt kept wet. The bottom of the box is so constructed as to hold 
water, and the sides are provided with cleats for holding glass shelves 
on which to place the briquettes. Care should be taken to keep 
the air in the closet uniformly moist, After 24 hours in moist air the 
test pieces for longer periods of time should be immersed in water 
maintained as near 21° Cent. (70° Fahr.) as practicable; they may 
be stored in tanks or pans, which should be of non-corrodible material. 



32 



MASONRY AND REINFORCED CONCRETE 



57. Tensile Strength. The tests may be made on any standard 
machine. A solid metal clip, as shown in Fig. 5, is recommended. 
This clip is to be used without cushioning at ihe points of contact 
with the test specimen. The bearing at each point of contact should 
be J-inch wide, and the distance between the center of contact on the 

same clip should be 1J inches. Test pieces 
should be broken as soon as they are removed 
from the water. Care should be observed in 
centering the briquettes in the testing machine, 
as cross-strains, produced by improper center- 
ing, tend to lower the breaking strength. The 
load should not be applied too suddenly, as it 
may produce vibration, the shock from which 
often breaks the briquette before the ultimate 
strength is reached. Care must be taken that 
the clips and the sides of the briquette be clean 
and free from grains of sand or dirt, which 
would prevent a good bearing. The load should 
be applied at the rate of 600 lbs. per minute. 
The average of the briquettes of each sample 
tested should be taken as the test, excluding 
any results which are manifestly faulty. 

58. Constancy of Volume. The object is to develop those quali- 
ties which tend to destroy the strength and durability of a cement. As 
it is highly essential to determine such qualities at once, tests of this 
character are for the most part made in a very short time, and are 
known, therefore, as accelerated tests. Failure is revealed by crack- 
ing, checking, swelling, or disintegration, or all of these phenomena. 
A cement which remains perfectly sound is said to be of constant 
volume. 

Methods. Tests for constancy of volume are divided into two 
classes : 

(1) Normal tests, or those made in either air or water maintained 
at about 21° Cent. (70° Fahr.). 

(2) Accelerated tests, or those made in air, steam, or water at a 
temperature of 45° Cent. (115° Fahr.) and upward. The test pieces 
should be allowed to remain 24 hours in moist air before immersion 
in water or steam, or preservation in air. For these tests, pats, 




Fig. 5. Metal Clip for 

Testing Tensile 

Strength. 



MASONRY AND REINFORCED CONCRETE 33 



about 7 \ cm. (2.95 in.) in diameter, l\ cm. (0.49 in.) thick at the 
center, and tapering to a thin edge, should be made, upon a clean 
glass plate [about 10 cm. (3.94 in.) square], from cement paste of 
normal consistency. 

Normal Test. A pat is immersed in water maintained as near 
21° Cent. (70° Fahr.) as possible for 28 days, and observed at inter- 
vals. A similar pat is maintained in air at ordinary temperature 
and observed at intervals. 

Accelerated Test. A pat is exposed in any convenient way in 
an atmosphere of steam, above boiling water, in a loosely closed 
vessel, for 3 hours. 

To pass these tests satisfactorily, the pats should remain firm 
and hard, and show no signs of cracking, distortion, or disintegration. 
Should the pat leave the plate, distortion may be detected best with 
a straight-edge applied to the surface which was in contact with the 
plate. In the present state of our knowledge it cannot be said that 
cement should necessarily be condemned simply for failure to pass 
the accelerated tests; nor can a cement be considered entirely satis- 
factory, simply because it has passed these tests. 

59. General Conditions. The committee recommends that: 

All cement shall be inspected. 

Cement may be inspected either at the place of manufacture or on the 
work. 

In order to allow ample time for inspecting and testing, the cement 
should be stored in a suitable weather-tight building having the floor properly- 
blocked or raised from the ground. 

The cement shall be stored in such a manner as to permit easy access 
for proper inspection and identification of each shipment. 

Every facility shall be provided by the contractor, and a period of at 
least twelve days allowed for the inspection and necessary tests. 

Cement shall be delivered in suitable packages, with the brand and 
name of manufacturer plainly marked thereon. 

A bag of cement shall contain 94 pounds of cement, net. Each barrel 
of Portland cement shall contain 4 bags, and each barrel of natural cement 
shall contain 3 bags of the above net weight. 

Cement failing to meet the 7-day requirements may be held awaiting 
the results of the 28-day tests, before rejection. 

All tests shall be made in accordance with the methods proposed by 
the Committee on Uniform Tests of Cement of the American Society of Civil 
Engineers, presented to the Society January 21, 1903, and amended January 
20, 1904, with all subsequent amendments thereto. 

The acceptance or rejection shall be based on the following re- 
quirements: 



34 MASONRY AND REINFORCED CONCRETE 

NATURAL CEMENT 

60. Definition. This term shall be applied to the finely pul- 
verized product resulting from the calcination of an argillaceous 
limestone at a temperature only sufficient to drive off the carbonic 
acid gas. 

61. Specific Gravity. The specific gravity of the cement 
thoroughly dried at 100° C, shall be not less than 2.8. 

62. Fineness. It shall leave by weight a residue of not more 
than 10 per cent on the No. 100, and 30 per cent on the No. 200 sieve. 

63. Time of Setting. It shall develop initial set in not less than 
ten minutes, and hard set in not less than thirty minutes, nor more 
than three hours. 

64. Tensile Strength. The minimum requirements for tensile 
strength for briquettes one inch square in cross-section, shall be within 
the following limits, and shall show no retrogression in strength 
within the periods specified: 

Neat Cement 
Age Strength 

24 hours in moist air 50-100 lbs, 

7 days (1 day in moist air, 6 days in water) 100-200 " 

28 days (1 day in moist air, 27 days in water) 200-300 " 

One Part Cement, Three Parts Standard Sand 

7 days (1 day in moist air, 6 days in water) 25- 75 " 

28 days (1 day in moist air, 27 days in water) 75-150 " 

65. Constancy of Volume. Pats of neat cement about three 
inches in diameter, one-half inch thick at the center, and tapering to 
a thin edge, shall be kept in moist air for a period of twenty-four 
hours. 

(a) A pat is then kept in air at normal temperature. 

(b) Another is kept in water maintained as near 70° F. as 
practicable. 

These pats are observed at intervals for at least 28 days, and, 
to pass the tests satisfactorily, should remain firm and hard and 
show no signs of distortion, cracking, or disintegrating. 

PORTLAND CEMENT 

66. Definition. This term is applied to the finely pulverized 
product resulting from the calcination to incipient fusion of an 
intimate mixture of properly proportioned argillaceous and cal- 



MASONRY AND REINFORCED CONCRETE 35 

careous materials, to which no addition greater than 3 per cent has 
been made subsequent to calcination. 

67. Specific Gravity. The specific gravity of the cement, 
thoroughly dried at 100° C, shall be not less than 3. 10. 

68. Fineness. It shall leave by weight a residue of not more 
than 8 per cent on the No. 100 sieve, and not more than 25 per cent 
on the No. 200 sieve. 

69. Time of Setting. It shall develop initial set in not less 
than thirty minutes, and must develop hard set in not less than one 
hour nor more than ten hours. 

70. Tensile Strength. The minimum requirements for tensile 
strength for briquettes one inch square in section, shall be within the 
following limits, and shall show no retrogression in strength within 
the periods specified: 

Neat Cement 
Age Strength 

24 hours in moist air 150-200 lbs. 

7 days (1 day in moist air, 6 days in water) 450-550 " 

28 days (1 day in moist air, 27 days in water) 550-650 " 

One Part Cement, Three Parts Sand 

7 days (1 day in moist air, 6 days in water) 150-200 " 

28 days (1 day in moist air, 27 days in water) 200-300 " 

Constancy of Volume. Pats of neat cement about three inches 
in diameter, one-half inch thick at the center, and tapering to a thin 
edge, shall be kept in moist air for a period of twenty-four hours. 

(a) A pat is then kept in air at normal temperature and ob- 
served at intervals for at least 28 days. 

(b) Another pat is kept in water maintained as near 70° F. as 
practicable, and observed at intervals for at least 28 days. 

(c) A third pat is exposed in any convenient way in an atmos- 
phere of steam, above boiling water, in a loosely closed vessel, for 
five hours. 

These pats, to pass the requirements satisfactorily, shall remain 
firm and hard, and show no signs of distortion, checking, cracking, or 
disintegrating. 

71. Sulphuric Acid and Magnesia. The cement shall not con- 
tain more than 1.75 per cent of anhydrous sulphuric acid (S0 3 ), 
and not more than 4 per cent of magnesia (MgO). 

72. Testing Machines. There are many varieties of testing 



36 



MASONRY AND REINFORCED CONCRETE 



machines on the market. Many engineers have constructed "home- 
made" machines which serve their purpose with sufficient accuracy. 
One very common type of machine is illustrated in Fig. 6. B is a reser- 
voir containing shot, which falls through the pipe I, which is closed 

with a valve at the 
bottom. The briquette 
is carefully placed be- 
tween the clips, as 
shown in the figure, 
and the wheel P is 
turned until the indi- 
cators are in line. The 
hook lever Y is moved 
so that a screw worm 
is engaged with its 
gear. Then open the 
automatic valve J so 
as to allow the shot to 
run into the cup F. 
By means of a small 
valve, the flow of shot 
into the cup may be 
regulated. Better re : 
suits will be obtained 
by allowing the shot 
to run slowly into the 
cup. The crank is then 
turned with just suf- 
ficient speed so that the scale beam is held in position until the 
briquette is broken. Upon the breaking of the briquette, the scale 
beam falls, and automatically closes the valve J. The weight of 
the shot in the cup F then indicates, according to some definite 
ratio, the stress required to break the briquette. 

SAND 

73. Sand is nearly always a constituent part of mortar and 
concrete. The strength of the masonry is dependent to a consider- 
able extent on the qualities of the sand, and it is therefore important 
that the desirable and the defective qualities should be understood. 




Fig. 6. Cement Testing Machine. 




DRIVING A "RAYMOND" CONCRETE PILE 
The pile is here being driven into the previously driven steel shell. 



MASONRY AND REINFORCED CONCRETE 37 

74. Object. The chief object of the sand is economy. If the 
joints between stones, especially in rubble masonry, were filled with 
a paste of neat cement, the cost would be excessive, and the increase 
in the strength of the masonry, if any, would be utterly dispropor- 
tionate to the great increase in cost. Secondly, the use of sand is a 
practical necessity in lime mortar, since neat lime, will contract and 
crack very badly when it hardens. 

75. Essential Qualities. The word "sand" as used above is 
intended as a generic term to apply to any finely divided material 
which will not- injuriously affect the cement or lime, and which is not 
subject to disintegration or decay. Sand is almost the only ma- 
terial that is sufficiently cheap, which will fulfil these requirements, 
although stone screenings (the finest material coming from a stone 
crusher), powdered slag, and even coal dust have occasionally been 
used as substitutes. Specifications usually demand that the sand 
shall be ' 'sharp, clean, and coarse, " and such terms have been re- 
peated so often that they are accepted as standard notwithstanding 
the frequent demonstration that modifications of these terms are 
not only desirable but also economical. These words also ignore 
other qualities which should be considered, especially when deciding 
between two or more different sources of sand supply. 

76. Geological Character. Quartz sand is the most durable 
and unchangeable Sands which consist largely of grains of feld- 
spar, mica, hornblende, etc., which will decompose upon prolonged 
exposure to the atmosphere, are less desirable than quartz, although, 
after being made up into the mortar, they are virtually protected 
against further decomposition. 

77. Coarseness. A mixture of coarse and fine grains, with 
the coarse grains predominating, is found very satisfactory, as it 
makes a denser and stronger concrete with a less amount of cement 
than when coarse-grained sand is used with the same proportion of 
cement. The small grains of sand fill the voids caused by the coarse 
grains so that there is not so great a volume of voids to be filled by 
the cement. The sharpness of sand can be determined approxi- 
mately by rubbing a few grains in the hand or by crushing it near 
the ear and noting if a grating sound is produced; but an examina- 
tion through a small lens is better. 

78. Sharpness. Experiments have shown that round grains of 



38 MASONRY AND REINFORCED CONCRETE 

sand have less voids than angular ones, and that water- worn sands 
have from 3 per cent to 5 per cent less voids than corresponding sharp 
grains. In many parts of the country where it is impossible, except at 
a great expense, to obtain the sharp sand, the round grain is used with 
very good results. Laboratory tests made under conditions as nearly 
as possible identical, show that the rounded-grain sand gives as good 
results as the sharp sand. In consequence of such tests, the re- 
quirement that sand shall be sharp is now considered useless by 
many engineers, especially when it leads to additional cost. 

79. Cleanness. In all specifications for concrete work, is found 
the clause: "The sand shall be clean. " This requirement is some- 
times questioned, as experimenters have found that a small per- 
centage of clay or loam often gives better results than when clean sand 
is used. "Lean" mortar may be improved by a small percentage of 
clay or loam, or by using dirty sand, for the fine material increases the 
density. In rich mortars, this fine material is not needed, as the 
cement furnishes all the fine material necessary, and if clay or loam 
or dirty sand were used, it might prove detrimental. Whether it is 
really a benefit or not, depends chiefly upon the richness of the con- 
crete and the coarseness of the sand. Some idea of the cleanliness 
of sand may be obtained by placing it in the palm of one hand and 
rubbing it with the fingers of the other. If the sand is dirty, it 
will badly discolor the palm of the hand. When it is found nec- 
essary to use dirty sand, the strength of the concrete should be 
tested. 

Sand containing loam or earthy material is cleansed by wash- 
ing with water, either in a machine specially designed for the pur- 
pose, or by agitating the sand with water in boxes provided with 
holes to permit the dirty water to flow away. 

Very fine sand may be used alone, but it makes a weaker con- 
crete than either coarse sand or coarse and fine sand mixed. A 
mortar consisting of very fine sand and cement will not be so dense 
as one of coarse sand and the same cement, although, when measured 
or weighed dry, both contain the same proportion of voids and 
solid matter. In a unit measure of fine sand, there are more grains 
than in a unit measure of coarse sand, and therefore more points of 
contact. More water is required in gauging a mixture of fine sand 
and cement than in a mixture of coarse sand and the same cement. 



MASONRY AND REINFORCED CONCRETE 39 

The water forms a film and separates the grains, thus producing a 
larger volume having less density. 

The screenings of broken stone are sometimes used instead of 
sand. Tests frequently show a stronger concrete when screenings 
are used than when sand is used. This is perhaps due to the vari- 
able sizes of the screenings, which would have a less percentage 
of voids. 

80. Percentage of Voids. As before stated, a mortar is strongest 
when composed of fine and coarse grains mixed in such proportion 
that the percentage of voids shall be the least. The simplest method 
of comparing two sands is ito weigh a certain gross volume of each, 
the sand having been thoroughly shaken down. Assuming that the 
stone itself of each kind of sand has the same density, then the heavier 
volume of sand will have the least percentage of voids. The actual 
percentage of voids in packed sand may be approximately determined 
by measuring the volume of water which can be added to a given 
volume of packed sand. If the water is poured into the sand, it is 
quite certain that air will remain in the voids in the sand, which will 
not be dislodged by the water, and the apparent volume of voids will 
be less than the actual. The precise determination involves the 
measurement of the specific gravity of the stone of which the sand 
is composed, and the percentage of moisture in the sand, all of which 
is done with elaborate precautions. Ordinarily such precise deter- 
minations are of little practical value, since the product of any one 
sandbank is quite variable. While it would be theoretically possible 
to mix fine and coarse sand, varying the ratios according to the vary- 
ing coarseness of the grains as obtained from the sand-pit, it is quite 
probable that an over-refinement in this particular would cost more 
than the possible saving is worth. Ordinarily sand has from 28 to 
40 per cent of voids. An experimental test of sand of various degrees 
of fineness, 12J per cent of it passing a No. 100 sieve, showed only 
22 per cent of voids; but such a value is of only theoretical interest. 

BROKEN STONE 

81. This term ordinarily signifies the product of a stone crusher 
or the result of hand-breaking by hammering large blocks of stone; 
but the term may also include gravel, described below. 

82. Classification of Stones. The best, hardest, and most 



40 MASONRY AND REINFORCED CONCRETE 

durable broken stone comes from the trap rocks, which are dark, 
heavy, close-grained rocks of igneous origin. The term granite is 
usually made to include not only true granite, but also gneiss, mica 
schist, syenite, etc. These are just as good for concrete work, and 
are usually less expensive. Limestone is suitable for some kinds of 
concrete work; but its strength is not so great as that of granite or 
trap rock, and it is more affected by a conflagration. Conglomerate, 
often called pudding stone, makes a very good concrete stone. The 
value of sandstone for concrete is very variable according to its tex- 
ture. Some grades , are very compact, hard, and tough, and make a 
good concrete; other grades are friable, and, like shale and slate, are 
practically unfit for use. Gravel consists of pebbles of various sizes, 
produced from stones which have been broken up and then worn 
smooth with rounded corners. The very fact that they have been 
exposed for indefinite periods to atmospheric disintegration and 
mechanical wear, is a proof of the durabilty and mechanical strength 
of the stone. 

83. Size of Stone and its Uniformity. There is hardly any 
limitation to the size of stone which may be used in large blocks of 
massive concrete, since it is now frequently the custom to insert 
these large blocks and fill the spaces between them with a concrete 
of smaller stone. But the term broken stone should be confined to 
those pieces of a size which may be readily mixed up in a mass, as is 
done when mixing concrete; and this virtually limits the size to stones 
which will pass through a 2j-inch ring. The lower limit in size is 
very indefinite, since the product of a stone crusher includes all sizes 
down to stone dust screenings, such as are substituted partially oi 
entirely for sand, as previously noted. Practically the only use of 
broken stone in masonry construction is in the making of concrete; 
and, since one of the most essential features of good concrete con- 
struction is that the concrete shall have the greatest possible density, 
it is important to reduce the percentage of voids in the stone as much 
as possible. This percentage can be determined with sufficient 
accuracy for ordinary unimportant work, by the very simple method 
previously described! for obtaining that percentage with sand — 
namely, by measuring how much water will be required to fill up the 
cavities in a given volume of dry stone. As before, such a simple 
determination is somewhat inexact, owing to the probability that 



MASONRY AND REINFORCED CONCRETE 41 



bubbles of air will, be retained in the stone which will reduce the 
percentage somewhat, and also because of the uncertainty involved 
as to whether the stone is previously dry or is saturated with water. 
Some engineers drop the stone slowly into the vessel containing the 
water, rather than pour the water into the vessel containing the 
stone, with the idea that the error due to the formation of air bubbles 
will be decreased by this method. The percentage of error, however, 
due to such causes, is far less than it is in a similar test of sand, and 
the error for ordinary work is too small to have any practical effect 
on the result. 

84. Example. A pail having a mean inside diameter of 10 
inches and a height of 14 inches is filled with broken stone well 
shaken down; a similar pail filled with water to a depth of 8 inches 
is poured into the pail of stone until the water fills up all the cavities 
and is level with the top of the stone; there is still 2 J inches depth 
of water in the pail. This means that a depth of 5f inches has been 
used to fill up the voids. The area of a 10-inch circle is 78 . 54 square 
inches and therefore the volume of the broken stone was 78.54 X 14 
= 1,099.56 cubic inches. The volume of the water used to fill the 
pail was 78.54 X 5.75, or 451.6 cubic inches. This is 41 per cent 
of the volume of the stone, and is in this case the percentage of voids. 
The accuracy of the above computation depends largely on the 
accuracy of the measurement of the mean inside diameter of the pail. 
If the pail were truly cylindrical, there would be no inaccuracy. If 
the pail is flaring, the inaccuracy might be considerable; and if a 
precise value is desired, more accurate methods should be chosen to 
measure the volume of the stone and of the water. 

It is invariably found that unscreened stone or the run of the 
crusher has a far less percentage of voids than screened stone, and 
it is therefore not only an extra expense, but also an injury to the con- 
crete, to specify that broken stone shall be screened before being used 
in concrete, unless, as described later, it is intended to mix definite pro- 
portions of several sizes of carefully screened broken stone. Since 
the proportion of large and small particles in the run of the crusher 
depends considerably upon the character of the stone which is being 
broken up, and perhaps to some extent on the crusher itself, these 
proportions should be tested at frequent intervals during the prog- 
ress of the work; and the amount of sand to be added to make a 



42 MASONRY AND REINFORCED CONCRETE 

good concrete should be determined by trial tests, so that the resulting 
percentage of voids shall be as small as it is practicable to make it. 
It is usually found that the percentage of voids in crusher-run granite 
is a little larger than in limestone or gravel. This gives a slight ad- 
vantage to the limestone and gravel, which tends to compensate for 
the weakness of the limestone and the rounded corners of the gravel. 

85. Broken stone is frequently sold by the ton, instead of by 
the cubic yard; but as its weight varies from 2,200 to 3,200 pounds 
per cubic yard, an engineer or contractor is uncertain as to how many 
cubic yards he is buying or how much it costs him per cubic yard, 
unless he is able to test the particular stone and obtain an average 
figure as to its weight per unit of volume. 

86. Cinders. Cinders for concrete should be free from coal or 
soot. Usually a better mixture can be obtained by screening the 
fine stuff from the cinders and then mixing in a larger proportion of 
sand, than by using unscreened material, although, if the fine stuff 
is uniformly distributed through the mass, it may be used without 
screening, and a less proportion of sand used. 

As shown later, the strength of cinder concrete is far less than 
that of stone concrete; and on this account it cannot be used where 
high compressive values are necessary. But on account of its very 
low cost compared with broken stone, especially under some con- 
ditions, it is used quite commonly for roofs, etc., on which the loads 
are comparatively small. 

One possible objection to the use of cinders lies in the fact that 
they frequently contain sulphur and other chemicals which may 
produce corrosion of the reinforcing steel. In any structure where 
the strength of the concrete is a matter of importance, cinders should 
not be used without a thorough inspection, and even then the unit 
compressive values allowed should be at a very low figure. 

MORTAR 

87. The term mortar is usually applied to the mixture of sand 
and cementing material which is placed between the large stones of a 
stone structure, although the term might also be properly applied to 
the matrix of the concrete in which broken stone is embedded. The 
object of the mortar is to furnish a cushion for the stones above 
it, which, as far as possible, distributes the pressure uniformly and 



MASONRY AND REINFORCED CONCRETE 43 

relieves the stones of transverse stresses and also from the concen- 
trated crushing pressures to which the projecting points of the stone 
would be subjected. 

88. Common Lime Mortar. The first step in the preparation 
of common lime mortar is the slaking of the lime. This should be 
done by putting the lime into a water-tight box, or at least on a plat- 
form which is substantially water-tight, and on which a sort of pond 
is formed by a ring of sand. The amount of water to be used should 
be from 2\ to 3 times the volume of the unslaked lime. 

The "volume" of unslaked lime is a very uncertain quantity, 
varying with the amount of settlement caused by mere shaking which 
it may receive during transit. A barrel of lime means 230 pounds. 
If the barrel has a volume of 3 . 75 cubic feet, it would be just filled 
by 230 pounds of lime when this lime weighed about 61 pounds per 
cubic foot. This same lime, however, may be so shaken that it will 
weigh 75 pounds per cubic foot, in which case its volume is reduced 
to 81 per cent, or 3.05 cubic feet. Combining this with 2\ to 3 times 
its volume of water, will require about 8 J cubic feet of water to one 
barrel of lime. On the other hand, if the lime has absorbed moisture 
from the atmosphere, and has become more or less air-slaked, its 
volume may become very materially increased. 

Although close accuracy is not necessary, the lime paste will be 
injured if the amount of water is too much or too little. In short, 
the amount of water should be as near as possible that which is chemi- 
cally required to hydrate the lime, so that on the one hand it shall be 
completely hydrated, and on the other hand it shall not be drowned 
in an excess of water which will injure its action in ultimate harden- 
ing. About three volumes of sand should be used to one volume of 
lime paste. Owing to the fact that the paste will, to a considerable 
extent, nearly fill the voids in the sand, the volume obtained from one 
barrel of unslaked lime made up into a mortar consisting of one part 
of lime paste to three parts of sand, will make about 6.75 barrels of 
mortar, or a little less than one cubic yard. 

89. Natural Cement Mortar. This is largely used, especially 
when mixed with lime to retard the setting, in the construction of 
walls of buildings, cellar foundations, and, in general, in masonry 
where the unit-stresses are so low that strength is a minor considera- 
tion, but where a lime mortar would not harden because it is to be 



44 



MASONRY AND REINFORCED CONCRETE 




Fig. 7. Bottomless Box for Measuring 
Sand. 



under water or in a solid mass where the carbonic acid of the at- 
mosphere could not penetrate to the interior. When natural cement 
is dumped loosely in a pile, the apparent volume is increased one- 
third or even one-half. This must be allowed for in mixing. A 

barrel averages 3.3 cubic feet. 
Therefore a 1 :4 mortar of natural 
cement would require one barrel 
of cement to 13.2 cubic feet 
(about one-half a cubic yard) of 
sand. A bottomless box similar 
to that illustrated in Fig. 7, and 
with inside dimensions of 3 feet 
X 2 feet 6 inches X 1 foot 9 
inches, contains 13.2 cubic feet. 
It is preferable to use even charges 
of one barrel of cement in mixing up a batch of mortar, rather than 
to dump it out and measure it loosely. If the size of the barrel varies 
from the average value given above, the size of the sand box should 
be varied accordingly. The barrels coming from any one cement 
mill may usually be considered as of uniform capacity. Since it is 
practically somewhat difficult to measure rccurately the volume of 
a barrel, owing to its swelling form, it is best to fill a sample barrel 
with loose, dry sand, and then to measure the volume of that sand by 
emptying it into a rectangular box whose inside area, together with 
the height of sand in it, can be readily measured. 

90. Portland Cement Mortar. A barrel of Portland cement 
will contain 370 to 380 pounds, net, of cement. Its capacity 
averages about 3.3 cubic feet, although with some brands the ca- 
pacity may reach 3.75. The expansion when the cement is thrown 
loosely in a pile or into a measuring box, varies from 10 to 40 per 
cent. The subject will be discussed further under the head of 
"Concrete." 

91. Lime in Cement Mortar. Lime is frequently employed 
in the cement mortar used for buildings, for a combination of reasons: 

(a) It is unquestionably more economical; but if the percentage added 
(or that which replaces the cement) is more than about 5 per cent, the strength 
of the mortar is sacrificed. The percentage of loss of strength depends on 
the richness of the mortar. 

(6) When used with a mortar leaner than 1:2, the substitution of 



MASONRY AND REINFORCED CONCRETE 45 



about 10 per cent of lime for an equal weight of cement will render concrete 
more water-tight, although at^some sacrifice in strength. 

(r) It always makes the mortar work more easily and smoothly. In 
fact, a rich cement mortar is very brash; it will not stick to the bricks or 
stones when striking a joint. It actually increases the output of the masons 
to use a mortar which is rendered smoother by the addition of lime. 

The substitution of more than 20 per cent of lime decreases the 
strength faster than the decrease in cost, and therefore should not 
be permitted unless strength is a secondary consideration and the 
combination is considered more as an addition of cement to a lime 
mortar in order to render it hydraulic. 

92. Effect of Re=gauging or Re=mixing Mortar. Specifications 
and textbooks have repeatedly copied from one another a requirement 
that all mortar which is not used immediately after being mixed and 
before it has taken an initial set must be rejected and thrown away. 
This specification is evidently based on the idea that after the initial 
set has been disturbed and destroyed, the cement no longer has the 
power of hardening, or at least that such power is very materially and 
seriously reduced. Repeated experiments, however, have shown 
that under some conditions the ultimate strength of the mortar 
(or concrete) is actually increased, and that it is not seriously injured 
even when the mortar is re-gauged several hours after being originally 
mixed with water. 

Such a specification against re-mixing is never applied to lime 
paste, since it is well known that a lime paste is considerably im- 
proved by being left for several days (or even months) before being 
used. This is evidently due to the fact that even during such a 
period the carbonic acid of the atmosphere cannot penetrate appreci- 
ably into the mass of the paste, while the greater length of time 
merely insures a more perfect slaking of the lime. The presence of 
free, unslaked lime in either lime or cement mortar is always injurious, 
because it generally results in expansion and disruption and possibly 
in injurious chemical reaction. 

Tests with Portland cement have shown that if it is re-mixed 
two hours after being combined with water, its strength, both ten- 
sile and compressive, is greater after six months' hardening, although 
it will be less after seven days' hardening, than in similar specimens 
which are moulded immediately after mixing. It is also found that 
the re-mixing makes the cement much slower in its setting. The 



46 MASONRY AND REINFORCED CONCRETE 

adhesion, moreover, is reduced by re-mixing, which is an important 
consideration in the use of reinforced concrete. 

The effects of tests with natural cement are somewhat contra- 
dictory, and this is perhaps the reason for the original writing of such 
a specification. The result of an elaborate series of tests made by 
Mr. Thomas F. Richardson showed that quick-setting cements 
which had been re-mixed showed a considerable falling off in strength 
in specimens broken after 7 days and 28 days of hardening, yet the 
ultimate strength after six months of hardening was invariably 
increased. It is also found that for both Portland and natural 
cements there is a very considerable increase in the strength of the 
mortar when it is worked continuously for two hours before mould- 
ing or placing in the masonry. Such an increase is probably due 
to the more perfect mixing of the constituents of the mortar. 

The conclusion of the whole matter appears to be, that when it 
is desirable that considerable strength shall be attained within a few 
days or weeks (as is generally the case, and especially so with rein- 
forced-concrete work), the specification against re-mixing should be 
rigidly enforced. For the comparatively few cases where a slow 
acquirement of the ultimate strength is permissible, re-mixing might 
be tolerated, although there is still the question whether the ex- 
pected gain in ultimate strength would pay for the extra work. It 
would be seldom, if ever, that this claimed property of cement 
mortar could be relied on to save a batch of mortar which would 
otherwise be rejected because it had been allowed to stand after 
being mixed until it had taken an initial set. 

93. Proportions of Materials for Mortar. (1) Lime Mortar. 
As previously stated in section 88, a barrel of unslaked lime should be 
mixed with about 8 J cubic feet of water. This will make about 9 
cubic feet of lime paste. Mixing this with a cubic yard of sand will 
make about 1 cubic yard of 1:3 lime mortar. This means approxi- 
mately 1 volume of unslaked lime to 8 volumes of sand. 

(2) Cement Mortars. The volume of cement depends very 
largely on whether it is loosely dropped in a pile, shaken together, 
or packed. The practical commercial methods of obtaining a mix- 
ture of definite proportions will be given later under "Concrete," 
section 94. Natural cement mortars are usually mixed in the 1 : 2 
ratio, although a 1 : 1 mixture would probably be used for tunnel 



MASONRY AND REINFORCED CONCRETE 47 

work or bridge abutments where natural cement would be used at all. 
Portland cement will be used to make 1 : 3 mortar for ordinary work, 
and 1 : 2 mortar for very high-grade work. As previously stated, a 
small percentage of lime is sometimes substituted for an equal volume 
of cement in order to make the mortar work better. 

CONCRETE 

Concrete is composed of a mixture of cement, sand, and crushed 
stone or gravel, which, after being mixed with water, soon sets and 
obtains a hardness and strength equal to that of a good building 
stone. These properties, together with its adaptability to mono- 
lithic construction, combined with its cheapness, render concrete 
very useful as a building material. 

94. General Principles of Proportioning Concrete. Theoretic- 
ally the proportioning of the sand and cementing material should be 
done by weight. It is always done in this way in laboratory testing. 
The volume of a given weight of cement is quite variable according 
as it is packed or loosely thrown in a pile. The same statement is 
true of sand. Since a barrel of Portland cement will increase in 
volume from 10 to 40 per cent by being merely dumped loosely in a 
pile and then shoveled into a measuring box, a contractor will fre- 
quently attempt to take advantage of this expansion by measuring 
the cement loose rather than by using the proportions as indicated 
by the original volume in the packed barrels. To a less extent the 
same uncertainty exists regarding the condition of the sand. Loose, 
dry sand occupies a considerably larger volume than wet sand, and 
this is still more the case when the sand is very fine. 

The general principle to be adopted is that the amount of water 
should be just sufficient to supply that needed for crystallization of the 
cement paste; that the amount of paste should be just sufficient to 
fill the voids between the particles of sand; that the mortar thus 
produced should be just sufficient to fill the voids between the broken 
stones. If this ideal could be realized, the total volume of the mixed 
concrete would be no greater than that of the broken stone. But no 
matter how thoroughly and carefully the ingredients are mixed and 
rammed, the particles of cement will get between the grains of sand 
and thus cause the volume of the mortar to be greater than that of the 
sand; the grains of sand will get between the smaller stones and 



48 MASONRY AND REINFORCED CONCRETE 

separate them; and the smaller stones will get between the larger 
stones and separate them. Experiments by Prof. I. O. Baker have 
shown that, even when the volume of the mortar was only 70 per cent 
of the volume of the voids in the broken stone, the volume of the 
rammed concrete was 5 per cent more than that of the broken stone. 
When the theoretical amount of mortar was added, the volume was 
7.5 per cent in excess, which shows that it is practically impossible 
to ram such concrete and wholly prevent voids. When mortar 
amounting to 140 per cent of the voids was used, all voids were 
apparently filled, but the volume of the concrete was 114 per cent of 
that of the broken stone. Therefore, on account of the impractica- 
bility of securing perfect mixing, the amount of water used is always 
somewhat in excess (which will do no harm); the cement paste is 
generally made somewhat in excess of that required to fill the par- 
ticles in the sand (except in those cases where, for economy, the 
mortar is purposely made very lean); and the amount of mortar is 
usually considerably in excess of that required to fill the voids in the 
stone. Even when we allow some excess in the above particulars, 
there is so much variation in the percentage of voids in the sand and 
broken stone, that the best work not only requires an experimental 
determination of the voids in the sand and stone which are being 
used; but, on account of the liability to variation in those percentages, 
even in materials from the same source of supply, the best work re- 
quires a constant testing and revision of the proportions as the work 
proceeds. For less careful work, the proportions ordinarily adopted 
in practice are considered sufficiently accurate. 

On the general principle that the voids in ordinary broken stone 
are somewhat less than half of the volume, it is a very common prac- 
tice to use one-half as much sand as the volume of the broken stone. 
The proportion of cement is then varied according to the strength 
required in the structure, and according to the desire to economize. 
On this principle we have the familiar ratios 1:2:4, 1:2J:5, 
1:3:6, and 1:4:8. It should be noted that in each of these cases, 
in which the numbers give the relative proportions of the cement, 
sand, and stone respectively, the ratio of the sand to the broken stone 
is a constant, and. the ratio of the cement is alone variable, for it 
would be just as correct to express the ratios as follows: 1:2:4; 
0.8:2:4; 0.07:2:4; 0.5:2:4. 




COMPLETED CONCRETE PILES 

The five piles in the center are to serve as the foundation for a chimney. A comparison with 
the barrel shown in the picture will give an accurate idea of the size of the piles. 




DRIVING A "RAYMOND" CONCRETE PILE 

The concrete core is held up between the leaders, ready to be driven. The steel shell on the 
right Is drawn up high enough to be lowered into the shell just driven and then slipped up on the 
core. 



MASONRY AND REINFORCED CONCRETE 



49 



95. Compressive Strength. The compressive strength of con- 
crete is very important, as it is used more often in compression than 
in any other way. It is rather difficult to give average values of 
the compressive strength of concrete, as it is dependent on so many 
factors. The available aggregates are so varied, and the methods 
of mixing and manipulation so different, that tests must be studied 
before any conclusions can be drawn. For extensive work, tests 
should be made with the materials available to determine the 
strength of concrete, under Conditions as nearly as possible like those 
in the actual structure. 

A series of experiments made at the Watertown Arsenal for 
Mr. George A. Kimball, Chief Engineer of the Boston Elevated 
Railway Company, in 1899, was one of the best sets of tests that have 
been published, and the results are given in Table III. Portland 
cement, coarse, sharp sand, and stone up to 2h inches were used; and 
when thoroughly rammed, the water barely flushed to the surface. 

TABLE III 
Compressive Strength of Concrete* 

Tests Made at Watertown Arsenal, 1899 





Brand of Cement 


Strength (Pounds per Square Inch) 




7 Days 


1 Month 


3 Months 


6 Months 


! 

1:2:4 \ 

1 


Saylor 

Atlas 

Alpha 

Germania 

Alsen 

Average 

Saylor 

Atlas 

Alpha 

Germania 

Alsen 

Average 


1,724 
1,387 
904 
2,219 
1,592 


2,238 
2,428 
2,420 
2,642 
2,269 


2,702 
2,966 
3,123 
3,082 
2,608 


3,510 
3,953 
4,411 
3,643 
3,612 




1,565 


2,399 


2,896 


3,826 


1:3:6 ■ 


1,625 
1,050 
892 
1,550 
1,438 


2,568 
1,816 
2,150 
2,174 
2,114 


2,882 
1,538 
2,355 
2,486 
2,349 


3,567 
3,170 
2,750 
2,930 
3,026 




1,311 


2,164 


2,522 


3,088 



*From "Tests of Metals," 1899. 

The values obtained in these tests are exceedingly high, and cannot be 
safely counted on in practice. 



50 MASONRY AND REINFORCED CONCRETE 

Tests made by Prof. A. N. Talbot (University of Illinois, Bul- 
letin No. 14) on 6-inch cubes of concrete, show the average values 
given in Table IV. The cubes were about 60 days old when tested. 

TABLE IV 

[^Compressive Tests of Concrete 

University'of Illinois 



No. of Tests 


Mixture 


Strength (Pounds per Square 
Inch) 


3 
6 

7 


1:2:4 

1:3:5} 

1:3:6 


2,350 
1,920 
1,300 



With fair conditions as to the character of the materials and 
workmanship, a mixture of 1:2:4 concrete should show a com- 
pressive strength of 2,000 to 2,300 pounds per square inch in 40 to 
60 days; a mixture of 1 : 2J: 5 concrete, a strength of 1,800 to 2,000 
pounds per square inch; and a mixture of 1:3:6 concrete, a strength 
of 1,500 to 1,800 pounds per square inch. The rate of hardening 
depends upon the consistency and the temperature. 

96. Tensile Strength. The tensile strength of concrete is usually 
considered about one-tenth of the compressive strength; that is, 
concrete which has a compressive value of 2,000 pounds per square 
inch should have a tensile strength of about 200 pounds per square 
inch. Although there is no fixed relation between the two values, 
the general law of increase in strength due to increasing the per- 
centage of cement and the density, seems to hold in both cases. 

97. Shearing Strength. The shearing strength of concrete is 
important on account of its intimate relation to the compressive 
strength and the shearing stresses to which it is subjected in struc- 
tures reinforced with steel. But few tests have been made, as they 
are rather difficult to make; but the tests made show that the shear- 
ing strength of concrete is nearly one-half the crushing strength. 
By shearing is meant the strength of the material against a sliding 
failure when tested as a rivet would be tested for shear. 

98. Modulus of Elasticity. The principal use of the modulus 
of elasticity in designing reinforced concrete is in determining the 
relative stresses carried by the concrete and the steel. The minimum 
value used in designing reinforced concrete is usually taken as 2,000,- 



MASONRY AND REINFORCED CONCRETE 51 

000, and the maximum value as 3,000,000, depending on the richness 
of the mixture used. A value of 2,500,000 is generally taken for 
ordinary concrete. 

99. Weight of Concrete. The weight of stone or gravel con- 
crete will vary from 145 pounds per cubic foot to 155 pounds per cubic 
foot, depending upon the specific gravity of the materials and the 
degree of compactness. The weight of a cubic foot of concrete is 
usually considered as 150 pounds. 

100. Cinder Concrete. Cinder concrete has been used to some 
extent on account of its light weight. The strength of cinder con- 
crete is from one-half to two-thirds the strength of stone concrete. 
It will weigh about 110 pounds per cubic foot. 

101. Rubble Concrete. Rubble concrete is a concrete in which 
large stones are placed, and will be discussed in Part II. 

102. Cost of Concrete. The cost of concrete depends upon the 
character of the work to be done, and the conditions under which it 
is necessary to do this work. The cost of the material, of course, 
will always have to be considered, but this is not so important as the 
character of the work. The cost of concrete in place will range from 
$4 . 50 per cubic yard to $20, or even $25, per cubic yard. When it is 
laid in large masses, so that the cost of forms is relatively small, the 
cost will range from $4.50 per cubic yard to $6 or $7 per cubic yard, 
depending on the local conditions and cost of materials. Founda- 
tions and heavy walls. are good examples of this class of work. For 
sewers and arches, the cost will vary from $7 to $13. In building 
construction — floors, roofs, and thin walls — the cost will range from 
$14 to $20 per cubic yard. 

103. Cost of Cement. The cost of Portland Cement varies 
with the demand. Being heavy, the freight is often a big item. The 
price varies from $1 to $2 per barrel. To this must be added the 
cost of handling. 

104. Cost of Sand. The cost of sand, including handling and 
freight, ranges from $0.75 to $1.50 per cubic yard. A common 
price for sand delivered in the cities is $1 .00 per cubic yard. 

105. Cost of Broken Stone or Gravel. The cost of broken 
stone delivered in the cities varies from $1.25 to $1.75 per cubic 
yard. The cost of gravel is usually a little less than stone. 

106. Cost of Mixing. Under ordinary conditions and where 



52 MASONRY AND REINFORCED CONCRETE 

the concrete will have to be wheeled only a very short distance, 
the cost of hand-mixing and placing will generally range from 
SO. 90 to SI .30 per cubic yard, if done by men skilled in this work. 
If a mixer is used, the cost will range from SO . 50 to SO . 90 per cubic 
yard. 

107. Cost of Forms. The cost of forms for heavy walls and 
foundations, varies from SO. 70 to SI. 20 per cubic yard of concrete 
laid. The cost of forms and mixing concrete will be further dis- 
cussed in Part IV. 

108. Practical Methods of Proportioning. A rich mixture, 
proportions 1:2:4 — that is, 1 barrel (4 bags) packed Portland 
cement (as it comes from the manufacturer), 2 barrels (7 .6 cubic feet) 
loose sand, and 4 barrels (15.2 cubic feet) loose stone — is used in 
arches, reinforced-conerete floors, beams, and columns for heavy 
loads; engine and machine foundations subject to vibration; tanks; 
and for water-tight work. 

A medium mixture, proportions 1 : 2h : 5 — that is, 1 barrel 
(4 bags) packed Portland cement, 2h barrels (9.5 cubic feet) loose 
sand, and 5 barrels (19 cubic feet) loose gravel or stone — may be 
used in arches, thin walls, floors, beams, sewers, sidewalks, founda- 
tions, and machine foundations. 

An ordinary mixture, proportions 1:3: 6 — that is, 1 barrel 
(4 bags) packed Portland cement, 3 barrels (11.4 cubic feet) loose 
sand, and 6 barrels (22 . 8 cubic feet) loose gravel or broken stone — 
may be used for retaining walls, abutments, piers, floor slabs, and 
beams. 

A lean mixture, proportions 1:4: 8 — that is, 1 barrel (4 bags) 
packed Portland cement, 4 barrels (15.2 cubic feet) loose sand, and 
8 barrels (30.4 cubic feet) loose gravel or broken stone — may be used 
in large foundations supporting stationary loads, backing for stone 
masonry, or where it is subject to a plain compressive load. 

These proportions must not be taken as always being the most 
economical to use, but they represent average practice. Cement 
is the most expensive ingredient; therefore a reduction of the quan- 
tity of cement, by adjusting the proportions of the aggregate so as 
to produce a concrete with the same density, strength, and imper- 
meability, is of great importance. By careful proportioning and 
workmanship, water-tight concrete has been made of a 1:3:6 



MASONRY AND REINFORCED CONCRETE 53 

mixture. In floor construction where the span is very short and it 
is specified that the slab must be at least 4 inches thick, while with 
a high-grade concrete a 3-inch slab would carry the load, it is cer- 
tainly more economical to use a leaner concrete. 

An accurate and simple method to determine the proportions 
of concrete is by trial batches. The apparatus consists of a scale 
and a cylinder which may be a piece of wrought iron pipe 10 inches 
to 12 inches in diameter capped at one end. Measure and weigh 
the cement, sand, stone, and w T ater and mix on a piece of sheet steel, 
the mixture having a consistency the same as to be used in the w T ork. 
The mixture is placed in the cylinder, carefully tamped, and the 
height to which the pipe is filled is noted. The pipe should be 
weighed before and after being filled so as to check the weight of 
the material. The cylinder is then emptied and cleaned. Mix 
up another batch using the same amount of cement and water, 
slightly varying the ratio of the sand and stone but having the same 
total weight as before. Note the height in the cylinder, which 
will be a guide to other batches to be tried. Several trials are made 
until a mixture is found that gives the least height in the cylinder, 
and at the same time works well while mixing, all the stones being 
covered with mortar, and which makes a good appearance. This 
method gives very good results, but it does not indicate the changes 
in the physical sizes of the sand and stone so as to secure the most 
economical composition as would be shown in a thorough mechan- 
ical analysis. 

There has been much concrete work done where the propor- 
tions were selected without any reference to voids, which has given 
much better results in practice than might be expected. The pro- 
portion of cement to the aggregate depends upon the nature of the 
construction and the required degree of strength, or water-tightness, 
as well as upon the character of the inert materials. Both strength 
and imperviousness increase with the proportion of cement to the 
aggregate. Richer mixtures are necessary for loaded columns, 
beams in building construction and arches, for thin walls subject 
to water pressure, and for foundations laid under water. The 
actual measurements of materials as actually mixed and used usually 
show leaner mixtures than the nominal proportions specified. This 
is largely due to the heaping of the measuring boxes. 



54 



MASONRY AND REINFORCED CONCRETE 



TABLE V 
Proportions of Cement, Sand, and Stone in Actual Structures 



Structure 


Proportions 


Reference 


C. B. & Q. R. R. 

Reinforced Concrete Culverts 






1:3:6 


Engi 


. Cont., Oct. 3, '06 


Phila. Rapid Transit Co. 

Floor Elevated Roadway 

c, . f Walls 

bub way | Floors _ 






1:3:6 

1:2.5:5 

1:3:6 

1:3:5 
1:4:7 


Cem( 


" Sept. 26, '06 


C. P. R, R. 
Arch Rings « 




Piers and Abutments 


mt Era, Aug. '06 


Hudson River Tunnel Caisson 






1:2:4 


Eng. 


Record, Sept. 29, '06 


Stand Pipe at Attleboro, Mass. 
Height, 106 feet. 






1:2:4 


u 


" 29, '06 


C.C.& St.L.R.R., Danville Arch 

Footings 

Arch Rings 

Abutments, Piers 


1:4 
1:2 
1:3 


:S 
4 
6 


or 1:9.5 
or 1:6.5 


(< 


" March 3, '06 


N. Y. C. & H. R. R. R. 

Ossining \(« 

Tunnel Icoping-.::::::::: 


1:4 
1:3 
1:2 


7.5 

6 
4 


<( 


11 "3, >06 


American Oak Leather Co. 
Factory at Cincinnati, Ohio. 






1:2:4 


u 


" * 8 3 ? '03 


Harvard University Stadium. . 






1:3:6 






New York Subway 

Roofs and Sidewalks 

Tunnel Arches 






1:2:4 
1:2.5:5 
1:2:4 
1:2.5:5 






Wet Foundation 2' th. or less 
" " exceeding 2' 




Boston Subway 






1:2.5:4 

1:2:4 
1:3:6 


(i 




P. & R. R. R, 
Arches 


" Oct. 13, '06 


Piers and Abutments 




Brooklyn Navy Yd. Laboratory 

Columns 

Beams and Slabs 

Roof Slab 


1:2 
1:3 
1:3 


: 3 Trap rock 

:5 " 

:5 Cinder 


Eng. 


News, March 23, '05 


Southern Railway 

Arches 

Piers and Abutments 


1:2 
1:2. 


:4 

5: 


5 







109. Methods of Mixing Concrete. The method of mixing 
concrete is immaterial, if a homogeneous mass is secured of a uniform 



MASONRY AND REINFORCED CONCRETE 



bb 



consistency, containing the cement, sand, and stone in the correct 
proportions. The value* of the concrete depends greatly upon the 
thoroughness of the mixing. The color of the mass must be uni- 
form, every grain of sand and piece of the stone should have cement 
adhering to every point of its surface. 



TABLE VI 

Barrels of Portland Cement Per Cubic Yard of Mortar 

(Voids in Sand Being 35 per cent and 1 Bbl. Cement Yielding 3.65 Cubic 



Feet of Cement 


Paste.) 










Proportion op Cement to Sand 


1:1 


1:1.5 


1:2 


1:2.5 


.1:3 


1:4 


Bbl. specified to be 3.5 cu. ft. ...... . 

" "' " 3.8 " 

<( u << 4Q u 

II a ti 44 (< 


Bbls. 
4.22 
4.09 
4.00 
3.81 


Bbls. 
3.49 
3.33 
3.24 
3.07 


Bbls. 
2.97 
2.81 
2.73 
2.57 


Bbls. 
2.57 
2.45 
2.36 
2.27 


Bbls. 
2.28 
2.16 
2.08 
2.00 


Bbls. 
1.76 
1.62 
1.54 
140 


Cu. yds. sand percu. yd. mortar. .. 


0.6 


0.7 


0.8 


0.9 


1.0 


1.0 



TABLE VII 

Barrels of Portland Cement Per Cubic Yard of Mortar 

(Voids in Sand Being 45 per cent and 1 Bbl. Cement Yielding 3.4 Cubic 
Feet of Cement P ste.) 



Proportion of Cement to Sand 


1:1 


1:1.5 


1:2 


1:2.5 


1:3 


1:4 


Bbl. specified to be 3.5 cu. ft 

" " " 3.8 " 

" " 40 " 

" " " 4.4 " 


Bbls. 

4.62 
4.32 
4.19 

3.94 


Bbls. 
3.80 
3.61 
3.46 
3.34 


Bbls. 
3.25 
3.10 
3.00 
2.90 


Bbls. 
2.84 
2.72 
2.64 
2.57 


Bbls. 
2.35 
2.16 
2.05 
1.86 


Bbls. 
1.76 
1.62 
1.54 
1.40 


Ou. yds. saud per cu. yds. mortar. . 


0.6 


0.8 


0.9 


1.0 


1.0 


1.0 



TABLE VIII 
Ingredients in 1 Cubic Yard of Concrete 

(Sand Voids, 40 per cent; Stone Voids, 45 per cent; Portland Cement Barrel 
Yielding 3.05 cu. ft. Paste. Barrel specified to be 3.8 cu. ft.) 



Proportions by Volumi 


1:2:4 


1:2:5 


1:2:6 


1 : 2.5 : 5 


1:2.5:6 


1:3:4 


Bbls. cement per. cu. yd. concrete. . 
Cu. vds. sand " " 
" stoue " " 


1.46 
0.41 

0.82 


1.30 
0.36 
0.90 


1.18 

0.33 
1.00 


1.13 

0.40 
0.80 


1.00 
0.35 

0.84 


1.25 
0.53 
0.71 


Proportions by volum 


1:3:5 


1:3:6 


1:3:7 


1:4:7 


1:4:8 


1:4:9 


Bbls. cement per ou. yd. concrete.. 
Cu. vds. sand " " 
" stone " " 


1.13 

0.48 
0.80 


1.05 
0.44 

0.88 


0.96 
0.40 
0.93 


0.82 
0.46 
0.80 


0.77 
0.43 
0.86 


0.73 
0.41 
0.92 



This table is to be used when cement is measured packed in the bar- 
Sel, for the ordinary barrel holds 3.8 cu. ft, 



56 



MASONRY AND REINFORCED CONCRETE 



TABLE IX 
Ingredients in 1 Cubic Yard of Concrete 

(Sand Voids, 40 per cent; Stone Voids, 45 per cent; Portland Cement 
Barrel Yielding 3.65 cu. ft. of Paste. Barrel specified to be 4.4 cu. ft.) 



Proportions by Volume 


1:2:4 


1:2:5 


1:2:6 


1:2.5:5 


1:2.5:6 


1:3:4 


Bbls. cement per cu. yd. concrete . . . 
Cu. yds. sand " " 
stone " " 


1.30 
0.42 

0.84 


1.16 
0.38 
0.95 


1.00 
0.33 
1.00 


1.07 
0.44 

0.88 


0.96 
0.40 
0.95 


1.08 
. 53 

0.71 


Proportions by volume 


1 :3:5 


1:3:6 


1:3:7 1:1:7 


1 :4:8 


1 :4:9 


Bbls. cement per cu. yd. concrete . . . 
Cu. yds. sand " " 
stone 


0.96 
0.47 

0.78 


0.90 
0.44 

0.88 


0.82 
0.40 
0.93 


0.75 
0.49 
0.86 


0.68 
0.44 
0.88 


0.64 
0.42 
0.95 



This table is to be used when the cement is measured loose, after 
dumping it into a box, for under such conditions a barrel of cement yields 
4.4 cu. ft. of loose cement. 

[Tables V to IX have been taken from Gillette's "Handbook of Cost Data."] 

110. Wetness of Concrete. In regard to plasticity, or facility 
of working and moulding, concrete may be divided into three classes : 
dry, medium, and very wet. 

Dry concrete is used in foundations which may be subjected to 
severe compression a few weeks after being placed. It should not be 
placed in layers of more than 8 inches, and should be thoroughly 
rammed. In a dry mixture the water will just flush to the surface 
only when it is thoroughly tamped. A dry mixture sets and will 
support a load much sooner than if a wetter mixture is used, and 
generally is used only where the load is to be applied soon after the 
concrete is placed. This mixture requires the exercise of more than 
ordinary care in ramming, as pockets are apt to be formed in the 
concrete; and one argument against it is the difficulty of getting a 
uniform product. 

Medium concrete will quake when rammed, and has the con- 
sistency of liver or jelly. It is adapted for construction work suited 
to the employment of mass concrete, such as retaining walls, piers, 
foundations, arches, abutments; and is sometimes also employed 
for reinforced concrete. 

A very wet mixture of concrete will run off a shovel unless it is 
handled very quickly. An ordinary rammer will sink into it of 



MASONRY AND REINFORCED CONCRETE 57 

— , 

its own weight. It is suitable for reinforced concrete, such as thin 
walls, floors, columns, tanks, and conduits. 

Within the last few years there has been a marked change in 
the amount of water used in mixing concrete. The dry mixture has 
been superseded by a medium or very wet mixture, often so wet as 
to require no ramming whatever. Experiments have shown that dry 
mixtures give better results in short time tests and wet mixtures in long 
time tests. In some experiments made on dry, medium, and wet 
mixtures it was found that the medium mixture was the most dense, 
wet next, and dry least. This experimenter concluded that the medium 
mixture is the most desirable, since it will not quake in handling, 
but will quake under heavy ramming. He found medium 1 per cent 
denser than wet and 9 per cent denser than dry concrete; he con- 
siders thorough ramming important. 

Concrete is often used so wet that it will not only quake but flow 
freely, and after setting it appears to be very dense and hard, but 
some engineers think that the tendency is to use far too much rather 
than too little water, but that thorough ramming is desirable. In 
thin walls very wet concrete can be more easily pushed from the 
surface so that the mortar can get against the forms and give a smooth 
surface. It has also been found essential that the concrete should 
be wet enough so as to flow under and around the steel reinforcement 
so as to secure a good bond between the steel and concrete. 

Following are the specifications (1903) of the American Rail- 
way Engineering and Maintenance of Way Association: 

"The concrete shall be of such consistency that when dumped 
in place it will not require tamping; it shall be spaded down and 
tamped sufficiently to level off and will then quake freely like jelly, 
and be wet enough on top to require the use of rubber boots by 
workman." 

111. Transporting and Depositing Concrete. Concrete is 
usually deposited in layers of 6 inches to 12 inches in thickness. In 
dandling and transporting concrete, care must be taken to prevent the 
separation of the stone from the mortar. The usual method of trans- 
porting concrete is by wheel-barrows, although it is often handled by 
cars and carts, and on small jobs it is sometimes carried in buckets. 
A very common practice is to dump it from a height of several feet 
^nto a trench. Many engineers object to this process as they claim 



53 



MASONRY AND REINFORCED CONCRETE 



C 



D 



J 



Fig. 8. Rammer 

for Dry Concrete. 

(Shoe 6 inches 

square.) 



that the heavy and light portions separate while falling and the con- 
crete is therefore not uniform through its mass, and they insist that 
it must be gently slid into place. A wet mixture is much easier to 
handle than a dry mixture, as the stone will not so 
readily separate from the mass. A very wet mixture 
has been deposited from the top of forms 43 feet 
high and the structure was found to be waterproof. 
On the other hand, the stones in a dry mixture will 
separate from the mortar on the slightest provoca- 
tion. Where it is necessary to drop a dry mixture 
several feet, it should be done by means of a chute 
or pipe. 

112. Ramming Concrete. Immediately after 
concrete is placed, it should be rammed or puddled, 
care being taken to force out the air-bubbles. The 
amount of ramming necessary depends upon how 
much water is used in mixing the concrete. If a 
very wet mixture is used, there is danger of too much 
ramming, which results in wedging the stones together and forcing 
the cement and sand to the surface. The chief object in ramming 
a very wet mixture is simply to expel the bubbles of air. 

The style of- rammer ordinarily used depends 
on whether a dry, medium, or very wet mixture is 
used. A rammer for dry concrete is shown in 
Fig. 8; and one for w T et concrete, in Fig. 9. In 
very thin walls, where a wet mixture is used, often 
the tamping or puddling is done with a part of 
a reinforcing bar. A common spade is often em- 
ployed for the face of work, being used to push 
back stones that may have separated from the 
mass, and also to work the finer portions of the 
mass to the face, the method being to work the 
spade up and down the face until it is thoroughly 
filled. Care must be taken not to pry with the 
spade, as this will spring the forms unless they 
are very strong. 

113. Bonding Old and New Concrete. To secure a water-tight 



j 



k3'ii 



>M"n 



Fig. 9. Rammer for 
Wet Concrete. 



joint between old and newconcrete, requires a great deal of care. Where 



MASONRY AND REINFORCED CONCRETE 59 

the strain is chiefly compressive, as in foundations, the surface of the 
concrete laid on the previous day should be washed with clean water, 
no other precautions being necessary. In walls and floors, or where 
a tensile stress is apt to be applied, the joint should be thoroughly 
washed and soaked, and then painted with neat cement or a mixture 
of one part cement and one part sand, made into a very thin mortar. 

In the construction of tanks or any other work that is to be 
water-tight, in which the concrete is not placed in one continuous 
operation, one or more square or V-shaped joints are necessary. 
These joints are formed by a piece of timber, say 4 inches by 6 inches, 
being imbedded in the surface of the last concrete laid each day. 
On the following morning, when the timber is removed, the joint is 
washed and coated with neat cement or 1 : 1 mortar. The joints may 
be either horizontal or vertical. The bond between old and new con- 
crete may be aided by roughening the surface after ramming or be- 
fore placing the new concrete. 

114. Effects of Freezing of Concrete. Many experiments 
have been made to determine the effect of freezing of concrete before 
it has a chance to set. From these and from practical experience, it 
is now generally accepted that the ultimate effect of freezing of Port- 
land cement concrete is to produce only a surface injury. The setting 
and hardening of Portland cement concrete is retarded, and the 
strength at short periods is lowered, by freezing; but the ultimate 
strength appears to be only slightly, if at all, affected. A thin scale 
about T V inch in depth is apt to scale off from granolithic or concrete 
pavements which have been frozen, leaving a rough instead of a 
troweled wearing surface ; and the effect upon concrete walls is often 
similar; but there appears to be no other injury. Concrete should 
not be laid in freezing weather, if it can be avoided, as this involves 
additional expense and requires greater precautions to be taken; 
but with proper care, Portland cement concrete can be laid at almost 
any temperature. 

There are three methods which may be used to prevent injury 
to concrete when laid in freezing weather: 

First: Heat the sand and stone, or use hot water in mixing the con- 
crete. 

Second; Add salt, calcium chloride, or other chemicals to lower the 
freezing point of the water. 



60 MASONRY AND REINFORCED CONCRETE 

Third: Protect the green concrete by enclosing it and keeping the 
temperature of the enclosure above the freezing point. 

The first method is perhaps more generally used than either of 
the others. In heating the aggregate, the frost is driven from it; 
hot water alone is insufficient to get the frost out of the frozen lumps 
of sand. If the heated aggregate is mixed with water which is hot 
but not boiling, experience has shown that a comparatively high 
temperature can be maintained for several hours, which will usually 
carry it through the initial set safely. The heating of the materials 
also hastens the setting of the cement. If the fresh concrete is 
covered with cairvas or other material, it will assist in maintaining 
a higher temperature. The canvas, however, must not be laid 
directly on the concrete, but an air space of several inches must be 
left between the concrete and the canvas. 

The aggregate is heated by means of steam pipes laid in the 
bottom of the bins, or by having pipes of strong sheet iron, about 
18 inches in diameter, laid through the bottom of the bins, and fires 
built in the pipes. The water may be heated by steam jets or other 
means. It is also well to keep the mixer warm in severe weather, by 
the use of a steam coil on the outside, and jets of steam on the 
inside. 

The second method — lowering the freezing point by adding 
salt- — has been commonly used to lower the freezing point of water. 
Salt will increase the time of setting and lower the strength of the 
concrete for short periods. There is a wide difference of opinion as 
to the amount of salt that may be used without lowering the ultimate 
strength of the concrete. Specifications for the New York Subway 
work required nine pounds of salt to each 100 pounds (12 gallons) of 
water in freezing weather. A common rule calls for 10 per cent of 
salt to the weight of water, which is equivalent to about 13 pounds 
of salt to a barrel of cement. 

The third method is the most expensive, and is used only in 
building construction. It consists in constructing a light wooden 
frame over the site of the work, and covering the frame with canvas 
or other material. The temperature of the enclosure is maintained 
above the freezing point by means of stoves. 



MASONRY AND REINFORCED CONCRETE 01 

115. Water=tightness of Concrete. Water-tight concrete, or 
concrete made water-tight by some kind of waterproof coating, is 
frequently required, either for inclosing a space which must be kept 
dry, or for storing water or other liquids. Concrete, even when 
most carefully prepared from materials of the highest grade, is never 
of itself completely waterproof. 

It is generally considered that in monolithic construction, a wet 
mixture, a rich concrete, and an aggregate proportioned for great 
density, are essential for water-tightness. With the wet mixtures of 
concrete now generally used in engineering work, concrete possesses 
far greater density, and is correspondingly less porous, than with the 
older, dryer mixtures. At the same time, in the large masses of actual 
work, it is difficult to produce concrete of such close texture as to 
prevent undesirable seepage at all points. Many efforts have been 
made to secure water-tightness of concrete in a practical manner — 
some with success, but others with unsatisfactory results. There 
are now a great many special preparations being advertised for 
making concrete water-tight. 

It has frequently been observed that when concrete was green, 
there was a considerable seepage through it, and that in a short time 
absolutely all seepage stopped. Some experiments have been made 
to render porous concrete impermeable, by forcing water through a 
rich concrete under pressure. In these experiments, a mixture of 
1 part Portland cement to 4 parts crushed gravel was used. The 
concrete tested was 6 inches thick. The flow through the concrete 
on the first day of the experiment, under a pressure of 36 pounds 
per square inch, w T as taken as 100 per cent. On the forty-sixth day, 
under a pressure of 48 pounds per square inch, the flow amounted 
to only 0.7 per cent. 

While the pressure was constant, the rate of seepage of the water 
decreased with the lapse of time, showing a marked tendency of the 
seepage passages to become closed. The experimenter is of the opin- 
ion that the water, under pressure, dissolves some of the material 
and t 1 en deposits it in stalactitic form near the exterior surface of the 
concrete, where the water escapes under much reduced pressure. 
Others, however, think it quite possible that fine material carried 
in suspension by the water aids in producing the result. 

For cistern work, two coats of Portland cement grout — 1 part 



62 MASONRY AND REINFORCED CONCRETE 

cement, 1 part sand — applied on the inside, have been found sufficient. 
About one inch of rich mortar has usually been found effective under 
high pressure. A coating of asphalt, or of asphalt with tarred or 
asbestos felt, laid in alternate layers between layers of concrete, has 
been used successfully. Coal-tar pitch and tarred felt, laid in alter- 
nate layers, have been used extensively and successfully in New York 
City for waterproofing. 

Mortar may be made practically non-absorbent by the addition 
of alum and potash soap. One per cent by weight of powdered alum 
is added to the dry cement and sand, and thoroughly mixed; and 
about one per cent of any potash soap (ordinary soft soap) is dissolved 
in the water used in the mortar. A solution consisting of 1 pound of 
concentrated lye, 5 pounds of alum, and 2 gallons of water, applied 
while the concrete is green and until it lathers freely, has been suc- 
cessfully used. Coating the surface with boiled linseed oil until 
the oil ceases to be absorbed, is another method that has been used 
with success. 

A reinforced concrete water-tank, 10 feet inside diameter and 
43 feet high, designed and constructed by W. B. Fuller at Little Falls, 
N. J., has some remarkable features. It is 15 inches thick at the 
bottom and 10 inches thick at the top. The tank was built in eight 
hours, and is a perfect monolith, all concrete being dropped from 
the top, or 43 feet at the beginning of the work. The concrete was 
mixed very wet, the mixture being 1 part cement, 3 parts sand, and 
7 parts broken stone. No plastering or waterproofing of any kind 
was used, but the tank was found to be absolutely water-tight - 
although the mixture used has not generally been found or considered 
water-tight. 

At Attleboro, Mass., a large reinforced concrete staMpipe, 50 
feet in diameter, 106 feet high from the inside of the bottom to the 
top of the cornice, and with a capacity of 1,500,000 gallons, has been 
constructed, and is in the service of the water works of that city. 
The walls of the standpipe are 18 inches thick at the bottom, and 8 
inches thick at the top. A mixture of 1 part cement, 2 parts sand, 
and 4 parts broken stone, the stone varying from -J inch to 1 \ inches, 
was used. The forms were constructed, and the concrete placed, in 
sections of 7 feet. When the walls of the tank had been completed, 
there was some leakage at the bottom with a head of water of 100 



MASONRY AND REINFORCED CONCRETE G3 

feet. The inside walls were then thoroughly cleaned and picked , 
and four coats of plaster applied. The first coat contained 2 per 
cent of lime to 1 part of cement and 1 part of sand; the remaining 
;hree coats were composed of 1 part sand to 1 part cement. Each 
coat was floated until a 'hard, dense surface was produced; [then it 
was scratched to receive the succeeding coat. 

On filling the standpipe after the four coats of plaster had been 
applied, the standpipe was found to be not absolutely water-tight. 
The water was drawn out; and four coats of a solution of castile soap, 
and one of alum, were applied alternately; and, under a 100-foot head, 
only a few leaks then appeared. Practically no leakage occurred 
at the joints; but in several instances a mixture somewhat wetter 
than usual was used, with the result that the spading and ramming 
served to drive the stone to the bottom of the batch being placed, 
and, as a consequence, in these places porous spots occurred. The 
joints were obtained . by inserting beveled tonguing pieces, and by 
thoroughly washing the joint and covering it with a layer of thin 
grout before placing additional concrete. 

In the construction of the filter plant at Lancaster, Pa., in 1905, 
a pure-water basin and several circular tanks were constructed of 
reinforced concrete. The pure-water basin is 100 feet wide by 200 
feet long and 14 feet deep, with buttresses spaced 12 feet 6 inches 
center to center. The walls at the bottom are 15 inches thick, and 
12 inches thick at the top. Four circular tanks are 50 feet in diameter 
and 10 feet high, and eight tanks are 10 feet in diameter and 10 
feet high. The walls are 10 inches thick at the bottom, and 
6 inches at the top. A wet mixture of 1 part cement, 3 parts sand, 
and 5 parts stone, was used. No waterproofing material was used, 
in the construction of the tanks; and when tested, two of them were 
found to be water-tight, and the other two had a few leaks where 
wires which had been used to hold the forms together had pulled out 
when the forms were taken down. These holes were stopped up and 
no furthur trouble was experienced. In constructing the floor of 
the pure-water basin, a thin layer of asphalt was used, as shown in 
Fig. 10; but no waterproofing material was used in the walls, and 
both were found to be water-tight. 

116. Sylvester Process. The alternate application of washes 
of castile soap and alum, each being dissolved in water, is known as 



64 



MASONRY AND REINFORCED CONCRETE 



Waterproofing) 







r -;:-j?.v-* 



Fig. 10. Floor of Pure- Water Basin. 



the Sylvester process of waterproofing. Castile soap is dissolved in 
water, j of a pound of soap in a gallon of water, and applied boiling 
hot to the concrete surface with a flat brush, care being taken not to 
form a froth. The alum dissolved in water — 1 pound pure alum in 8 
gallons of water — is applied 24 hours later, the soap having had time 

to become dry and hard. The 
second wash is applied in the 
same manner as the first, at a 
temperature of 60° to 70° F. The 
alternate coats of soap and alum 
are repeated * every 24 hours. 
Usually four coats will make an 
impervious coating. The soap 
and alum combine and form an 
insoluble compound, filling the pores of the concrete and prevent- 
ing the seepage of water. The walls should be clean and dry, and 
the temperature of the air not lower than 50° F., when the composi- 
tion is applied. The composition should be applied while the con- 
crete is still green. This method of waterproofing has been used 
extensively for years, and has generally given satisfactory results for 
moderate pressures. 

117. Asphalt Waterproofing. If asphalt is to be applied to a 
concrete surface, the concrete should be dry; and it will be found 
generally more satisfactory to coat the dry surface first with asphalt 
cut with naphtha. Unless the concrete is heated, it is generally very 
hard to make the asphalt adhere to the concrete. Hot asphalt 
applied to ordinary concrete surfaces will generally roll up like a 
blanket when it cools. The concrete should be heated by hot sand, 
or the asphalt should be cut with naphtha. When the coat con- 
taining the naphtha has been applied — like a coat of paint — and is 
dry, then the asphalt mastic is applied. The asphalt mastic is com- 
posed of 1 part asphalt to 4 parts of sand. This is smoothed off with 
hot irons, and thoroughly tamped into place. If stone or earth is 
to be placed next to the asphaltic surface, it is best to cover the sur- 
face with roofing gravel to protect the asphalt. 

Asphalt paint has been used for a protective coat for all kinds of 
masonry where earth is to be placed against it. 

A coat of asphalt j inch thick applied with mops to a grout 



MASONRY AND REINFORCED CONCRETE 



65 



surface, has been used satisfactorily for coating the interiors of tanks, 
for heads greater than 19 feet, by Mr. J. W. Schaub ("Transactions" 
of the American Society of Civil Engineers, Vol. LI). Mr. Schaub 
states that he believes the J-inch coat, in addition to the grout, is 
sufficient for a water pressure of GO feet. 

118. Felt Laid with Asphalt. In waterproofing floors, roofs, 
subways, tunnels, etc., alternate layers of paper or felt are laid with 
asphalt, bitumen, or tar. These materials range from ordinary tar 
paper laid with coal-tar pitch, to asbestos or asphalt felt laid in 
asphalt. Coal-tar products deteriorate when exposed to moisture. 
Some asphalts are more suitable than others for waterproofing pur- 
poses; therefore the properties of any asphalt intended for water- 
proofing should be thoroughly investigated. 

In using these materials for rendering concrete water-tight, 
usually a layer of concrete or brick is first laid. On this is mopped 
a layer of hot asphalt; felt or paper is then laid on the asphalt, the 
latter being lapped from 6 to 12 inches. After the first layer of felt 
is placed, it is mopped over with hot asphalt compound, and another 
layer of felt or paper is laid, the 
operation being repeated until 
the desired thickness is secured, 
which is usually from 2 to 10 
layers — or, in other words, the 
waterproofing varies from 2-ply 
to IQ-ply. A waterproofing 
course of this kind, or a course 
as described in the paragraph 
on asphalt waterproofing, forms 
a distinct joint, and the strength 
in bending of the concrete on the two sides of the layer must be 
considered independently. 

When asphalt, or asphalt laid with felt paper, is used for water- 
proofing the interiors of the walls of tanks, a 4-inch course of brick is 
required to protect and hold in place the waterproofing materials. 
Fig. 11 shows a wall section of a reservoir (Engineering Record, Sept. 
21, 1907) constructed for the New York, New Haven & Hartford 
Railroad, which illustrates the methods described above. The 
waterproofing materials for this reservoir consist of 4-ply "Hydrex" 



z 



f>i. 






> Ply Hydrex Felt- 









■«fc' 



Fig. 11. Method of Waterproofing Reservoir. 



66 



MASONRY AND REINFORCED CONCRETE 



felt, and "Hydrex" compound was used to cement the layers together. 
Fig. 12 is an illustration of the method used by the Barrett 
Manufacturing Company in applying their 5-ply coal-tar pitch and 
felt roofing material, and it shows in a general way the method of 
laying asphalt and felt for waterproofing purposes. The company's 
instructions for applying this roofing are as follows: 

"First coat the concrete (A) with hot pitch (B) mopped on uniformly. 
Over the above coating of pitch,, lay two thicknesses of tarred felt (C), 

lapping each sheet seventeen (17) 
inches over the preceding one, and 
mopping back with pitch (D) the 
full width of each lap. 

"Over the felt thus laid, spread a 
uniform coating of pitch (E) mopped 
on. Then lay three (3) full thick- 
nesses of tarred felt (F), lapping 
each sheet twenty-two (22) inches 
over the preceding one. 

"When the felt is thus laid, mop 
back with pitch (G) the full width 
of twenty-two (22) inches under 
each lap. Then spread over the en- 
tire surface of the roof a uniform 
coating of pitch, into which, while 
hot, imbed slag or gravel (H)." 

In applying asphalt and felt 
for general waterproofing pur- 
poses, the felt, as already stated, 
would be in a continuous roll, 
and not in sheets as shown for 
roofing purposes. 

119. Medusa Waterproof 
Compound. Among the many patented waterproofing materials 
on the market is the " Medusa." This compound is claimed to 
prevent efflorescence, as well as to make concrete waterproof. In 
using it, the following directions, given by the manufacturing com- 
pany, are to be observed : 

"To render cement work impervious to water, a small quantity of the 
compound is thoroughly mixed with the dry cement, before the addition of 
sand and water. For most purposes, from 1 to 2 per cent of the weight of 
cement used will be found sufficient. This is equivalent to from four to 
eight pounds of the compound to one barrel of cement. The precise amount 
to be used must be left to the experience of the user, and depends upon the 




Fig. 12. Five-Ply Gravel Roofing. 



MASONRY AND REINFORCED CONCRETE 67 



proportion of sand, etc., employed, and on the kind of work to be done. 
Our own experience has been that the use of 1 per cent — 4 pounds to the 
barrel, or 1 pound to the sack of cement — is enough to make hollow concrete 
building blocks water-tight. For cistern and reservoir linings and other 
work which must be absolutely impervious, a somewhat larger amount 
should be used. Thorough mixing is of the utmost importance." 

In the operation of waterproofing, a very common mistake is 
made in applying the waterproofing materials on the wrong side of 
the wall to be made water-tight. That is, if water finds its way 
through a cellar wall, it is generally useless to apply a waterproofing 
coat on the inside surface of the wall, as the pressure of the water 
will push it off. If, however, there is no great pressure behind it, 
a waterproofing coat applied on the inside of the wall is usually suc- 
cessful in keeping moisture out of the cellar. To be successful in 
waterproofing a cellar wall, the waterproofing material should be 
applied on the outside surface of the wall; and if properly applied , 
the wall, as well as the cellar, will be entirely free of water. 

In tank or reservoir construction, the conditions are different, 
in that it is desired to prevent the escape of water. In these cases, 
therefore, the waterproofing is applied on the inside surface, and is 
supported by the materials used in constructing the tank or reservoir. 
The structure should always be designed so that it can be properly 
waterproofed, and no asphaltic waterproofing should be laid at a 
temperature below 25° F. 

The above-described methods of waterproofing are applicable 
to stone and brick masonry as well as to concrete. 

BITUMEN 

120. Varieties. One of the groups of mineral substances com- 
posed of different hydro-carbons, which are widely scattered through- 
out the world, is known as bitumen. There is a great variety of 
forms in which bitumen is found, ranging from volatile liquids to 
thick semi-fluids and solids. These are usually intermixed with 
different kinds of inorganic or organic matter, but are sometimes 
found in a free or pure state. Liquid varieties are known as naphtha 
and petroleum; the viscous or semi-fluid as maltha or mineral tar; 
and the solid as asphalt or asphaltum. 

121. Asphaltum. The most noted deposit of asphaltum is 
found in the island of Trinidad and at Bermudez, Venezuela. De- 



68 MASONRY AND REINFORCED CONCRETE 



posits of nearly pure asphaltum are found in Utah, Mexico, Cuba 3 
and different parts of the United States. Varieties of nearly pure 
asphalt are known as wurtzilite, elaterite, and gilsonite. 

The main source of supply of asphaltum used in the United 
States for street paving, has been the Trinidad deposit. This is also 
the main source for asphaltic roofing materials. 

122. Asphalt. The bituminous limestone deposits at Seyssel 
and Pyrimont, France; in the Val-de-Travers, Canton of Neuchatel, 
Switzerland; and at Ragusa, Sicily, are known as rock asphalt. It 
is more durable than asphaltum, and is extensively used in Europe 
for paving purposes. 

There are two forms in which rock asphalt is prepared for ship- 
ment: 

(a) Compressed asphalt blocks, which are used in about the manner 
of stone blocks. 

(6) Mastic asphalt, which is made into blocks of different sizes, gener- 
ally bearing the manufacturer's trade mark. 

The mastic asphalt is used for waterproofing and damp-proofing 
purposes. For all work of this kind, the Val-de-Travers, or the 
Seyssel, or Sicilian rock asphalt should be used. 

PRESERVATION OF STEEL IN CONCRETE 

123. Tests have been made to find the value of Portland cement 
concrete as a protection of steel or iron from corrosion. Nearly all 
of these tests have been of short duration (from a few weeks to several 
months); but they have clearly shown, when the steel or iron is 
properly imbedded in concrete, that on being removed therefrom it 
is clean and bright. Steel removed from concrete containing cracks 
or voids usually shows rust at the points where the voids or cracks 
occur; but if the steel has been completely covered with concrete, 
there is no corrosion. Tests have shown that if corroded steel is 
imbedded in concrete, the concrete will remove the rust. To secure 
the best results, the concrete should be mixed quite wet, and care 
should be taken to have the steel thoroughly imbedded in the con- 
crete. 

124. Cinder vs. Stone Concrete. A compact cinder concrete 
has proven about as effective a protection for steel as stone concrete. 
The corrosion found in cinder concrete is mainly due to iron oxide 



MASONRY AND REINFORCED CONCRETE 69 



or rust in the cinders, and not to the sulphur. The amount of sul- 
phur in cinders is extremely small, and there seems to be little danger 
from that source. A steel-frame building erected in New York in 
1898 had all its framework, except the columns, imbedded in cinder 
concrete; when the building was demolished in 1903, the frame 
showed practically no rust which could be considered as having 
developed after the material was imbedded. 

12,"). Practical Illustrations. Cement washes, paints, and 
plasters have been used for a long time, in both the United States and 
Europe, for the purpose of protecting iron and steel from rust. The 
engineers of the Boston Subway, after making careful tests and 
investigations, adopted Portland cement paint for the protection of 
the steel work in that structure. The railroad companies of France 
use cement paint extensively to protect their metal bridges from 
corrosion. Two coats of the cement paint and sand are applied with 
leather brushes. 

A concrete-steel water main on the Monier system, 12 inches in 
diameter, 1 { \ inches thick, containing a steel framework of i-inch 
and T V-inch steel rods, was taken up after 15 years' use in wet ground, 
at Grenoble, France. The adhesion was found perfect, and the 
metal absolutely free from rust. 

William Sooy Smith, M. Am. Soc. C. E., states that in removing 
a bed of concrete at a lighthouse in the Straits of Mackinac, twenty 
years after it was laid, and ten feet below water surface, imbedded 
iron drift-bolts were found free from rust. 

A very good example of the preservation of steel imbedded in 

concrete is given by Mr. H. C. Turner (Engineering News, Jan. 10, 

1908). Mr. Turner's company has recently torn down a one-story 

reinforced-concrete building erected by his company in 1902, at New 

Brighton, Staten Island. The building had a pile foundation, the 

piles being cut off at mean tide level. The footings, side walls, 

columns, and roof were all constructed of reinforced concrete. The 

portion removed was 30 by 60 feet, and was razed to make room for 

a five-story building. In concluding his account, Mr. Turner says: 

"All steel reinforcement was found in perfect preservation, excepting 
in a few cases where the hoops were allowed to come closer than f inch to the 
surface. Some evidence of corrosion was found in such cases, thus demon- 
strating the necessity of keeping the steel reinforcement at least £ inch from 
the surface. The footings w T ere covered by the tide twice daily. The concrete 



70 MASONRY AND REINFORCED CONCRETE 

was extremely hard, and showed no weakness whatever from the action of 
the salt w T ater. The steel bars in the footings were perfectly preserved, even 
in cases where the concrete protection was only f inch thick." 

126. Tests by Professor Norton. Prof. Chas. L. Norton made 
several experiments with concrete bricks, 3 by 3 by 8-inch, in which 
steel rods, sheet metal, and expanded metal were imbedded. The 
specimens were enclosed in tin boxes with unprotected steel, and 
were exposed for three weeks. One portion was exposed to steam, 
air, and carbon dioxide; another to air and steam; another to air and 
carbon dioxide; and another was left in the testing room. In these 
tests, Portland cement was used. The bricks were made of neat 
cement of 1 part cement and 3 parts sand; of 1 part cement and 5 
parts stone; and of 1 part cement and 7 parts cinders. After the 
steel had been imbedded in these blocks three weeks, thev were 
opened and the steel examined and compared with specimens which 
had been unprotected in corresponding boxes in the open air. The 
unprotected specimens consisted of rather more rust than steel; 
the specimens imbedded in neat cement were found to be perfectly 
protected; the rest of the specimens showed more or less corrosion. 
Professor Norton's conclusions were as follows: 

1. Neat Portland cement is a very effective preventive against rusting. 

2. Concrete, to be effective in preventing rust, should be dense and 
without voids or cracks. It should be mixed wet when applied to steel. 

3. The corrosion found in cinder concrete is mainly due to iron oxide 
in the cinders, and not to sulphur. 

4. Cinder concrete, if free from voids and well rammed when wet, is 
about as effective as stone concrete. 

5. It is very important that the steel be clean when imbedded in 
concrete. 

FIRE PROTECTION 

127. The various tests which have been conducted — including 
the involuntary tests made as the result of fires — have shown that 
the fire-resisting qualities of concrete, and even resistance to a com- 
bination of fire and water, are greater than those of any other known 
type of building construction. Fires and experiments which test 
buildings of reinforced concrete have proved that where the tem- 
perature ranges from 1,400° to 1,900° F., the surface of the concrete 
may be injured to a depth of \ to \ inch or even of one inch; but 
the body of the concrete is not affected, and the only repairs re- 
quired, if any, consist of a coat of plaster. 



MASONRY AND REINFORCED CONCRETE 71 



128. Theory. The theory given by Mr. Spencer B. Newberry 
is that the fireproofing qualities of Portland cement concrete are due 
to the capacity of the concrete to resist fire and prevent its trans- 
ference to steel by its combined water and porosity. In hardening, con- 
crete takes up 12 to 18 per cent of the water contained in the cement. 
This water is chemically combined, and not given off at the boiling 
point. On heating, a part of the water is given off at 500° F., but 
dehydration does not take place until 900° F. is reached. The mass 
is kept for a long time at comparatively low temperature by the 
vaporization of water absorbing heat. A steel beam imbedded in 
concrete is thus cooled by the volatilization of water in the sur- 
rounding concrete. 

Resistance to the passage of heat is offered by the porosity of 
concrete. Air is a poor conductor, and an air space is an efficient 
protection against conduction. The outside of the concrete may 
reach a high temperature; but the heat only slowly and imperfectly 
penetrates the mass, and reaches the steel so gradually that it is 
carried off by the metal as fast as it is supplied. 

129. Cinder vs. Stone Concrete, Mr. Newberry says: "Porous 
substances, such as asbestos, mineral wool, etc., are always used as 
heat-insulating material. For this same reason, cinder concrete, 
being highly porous, is a much better non-conductor than a dense 
concrete made of sand and gravel or stone, and has the added ad- 
vantage of being light." 

Professor Norton, in comparing the actions of cinder and stone 
concrete in the great Baltimore fire of February, 1904, states that 
there is but little difference in the two concretes. The burning of bits 
of coal in poor cinder concrete is often balanced by the splitting of 
stones in the stone concrete. "However, owing to its density, the 
stone concrete takes longer to heat through." 

130. Thickness of Concrete Required for Fireproofing. Actual 
fires and tests have shown that 2 inches of concrete will protect an 
I-beam with good assurance of safety. Small rods in girders are more 
effectively coated, and 1J inches of concrete is usually considered 
sufficient protection, although some city building laws specify 2 
inches of concrete. Beams usually have the same thickness of con- 
crete for fireproofing purposes as the main girders, although perhaps 
1 to U inches would be sufficient. For ordinary slabs, J inch is 



72 MASONRY AND REINFORCED CONCRETE 

ample protection; but for long-span slabs the fireproofing thick- 
ness should be from f inch to 1J inches. Columns should have at 
least 2 inches of concrete outside of the steel; often 3 inches is speci- 
fied. 

131. The Baltimore Fire. Engineers and architects, who made 
reports on the Baltimore fire of February, 1904, generally state that 
reinforced concrete construction stood very well — much better than 
terra-cotta. Professor Norton, in his report to the Insurance Engi- 
neering Experiment Station, says : 

"Where concrete floor-arches and concrete-steel construction received 
the full force of the fire, it appears to have stood well, distinctly better than 
the terra-cotta. The reasons, I believe, are these: First, because the con- 
crete and steel expand at sensibly the same rate, and hence, when heated, 
do not subject each other to stress; but terra-cotta usually expands about 
twice as fast with increase in temperature as steel, and hence the partitions 
and floor-arches soon become too large to be contained by the steel members 
which under ordinary temperature properly enclose them." 

132. Fire and Water Tests. Under the direction of Prof. Francis 
C. Van Dyck, a test was made on December 26, 1905, on stone and 
cinder reinforced concrete, according to the standard fire and water 
tests of the New York Building Department. A building was con- 
structed 16 feet by 25 feet, with a wall through the middle. The 
roof consisted of the two floors to be tested. One floor was a rein- 
forced cinder concrete slab and steel I-beam construction; and the 
other was a stone concrete slab and beam construction. The floors 
were designed for a safe load of 150 pounds per square foot, w r ith a 
factor of safety of four. 

The object of the test was to ascertain the result of applying to 
these floors, first, a temperature of about 1,700° F. during four hours, 
a load of 150 lbs. per square foot being upon them; and second, a 
stream of water forced upon them while still at about the temperature 
above stated. A column was placed in the chamber roofed by the 
rock concrete, and it was tested the same way. 

The fuel used was seasoned pine wood, and the stoking was 
looked after by a man experienced in a pottery; hence a very even 
fire was maintained, except at first, on the cinder concrete side, where 
the blaze began in one corner and spread rather slowly for some time. 

The water was supplied from a pump at which 00 lbs. pressure 
was maintained, and was delivered through 200 feet of new cotton 



MASONRY AND REINFORCED CONCRETE 73 

hose and a 1 -J-inch nozzle. Each side was drenched with water while 
at full temperature, apparently; and the water was thrown as uni- 
formly as possible over the surface to be tested, for the required 
time. The floors were then flooded on top, and again treated 
underneath. 

Inasmuch as the floors and the column were the only parts sub- 
mitted for tests, the slight cracking and pitting of the walls and 
partition need not be detailed. 

The column was practically intact, except that a few small 
pieces of the concrete were washed out where struck by the stream 
at close range. The metal, however, remained completely covered. 
On the rock concrete side, the beams showed naked metal up to 
within about 7 inches of the ends on one beam, and about 2 feet 
from the ends on the other beam. The reinforcing bars were de- 
nuded over an area of about 30 square feet near the center; but no 
cracks developed, and the water poured on top seemed to come 
down only through the pipe set in for the pyrometer. 

On the cinder concrete side, the beams lost only a little of the 
edges of the covering, not showing the metal at all. There were no 
cracks on this side either, and the water came down through the 
pyrometer tube as on the other side. The metal in the.slab was bared 
over an area of about 24 square feet near the center. 

During the firing, both chambers were occasionally examined, 
and no cracking or flaking-off of the concrete could be detected. 
Hence the water did all the damage that was apparent at the 
end. 

During the test the floors supported the load they were designed 
to carry; and on the following day the loads were increased to 600 
pounds per square foot. 

The following is taken from Professor Van Dyck's report: 

"The maximum deflection of the stone concrete before the application 
of water, was 2\% inches; after application of water, 3 T 3 g inches; with normal 
temperature and original load, 3 T V inches; deflection after load of 600 pounds 
was added, 3^f inches. 

"The maximum deflection of the cinder concrete before the application 
of water, was 6^ inches; after application of water, Qh inches; with normal 
temperature and original load, 5\\ inches; deflection after a load of 600 
pounds was added, 6 inches. These measurements were taken at the center 
of the roof of each chamber." 



74 MASONRY AND REINFORCED CONCRETE 

METHODS OF MIXING 

133. The two methods used in mixing concrete are by hand 
and by machinery. Good concrete may be made by either method 
Concrete mixed by either method should be carefully watched by 
a good foreman. If a large quantity of concrete is required, it is 
cheaper to mix it by machinery. On small jobs where the cost of 
erecting the plant, together with the interest and depreciation, 
divided by the number of cubic yards to be made, constitute a large 
item, or if frequent moving is required, it is very often cheaper to mix 
the concrete by hand. The relative cost of the two methods usually 
depends upon circumstances, and must be worked out in each in- 
dividual case. 

134. Hand Mixing. The placing and handling of materials and 
arranging the plant are varied by different engineers and contractors. 
In general the mixing of concrete is a simple operation, but should be 
carefully watched by an inspector. He should see 

(1) That the exact amount of stone and sand are measured out; 

(2) That the cement and sand are thoroughly mixed; 

(3) That the mass is thoroughly mixed; 

(4) That the proper amount of water is used; 

(5) That care is taken in dumping the concrete in place; 

(6) That it is thoroughly rammed. 

The mixing platform, which is usually 10 to 20 feet square, 
is made of 1-inch or 2-inch plank planed on one side and well nailed 
to stringers, and should be placed as near the work as possible, but 
so situated that the stone can be dumped on one side of it and the 
sand on the opposite side. A very convenient way to measure the 
stone and sand is by the means of bottomless boxes. These boxes 
are of such a size that they hold the proper proportions of stone 
or sand to mix a batch of a certain amount. Cement is usually 
measured by the package, that is by the barrel or bag, as they con- 
tain a definite amount of cement. 

The method used for mixing the concrete has little effect upon 
the strength of the concrete, if the mass has been turned a sufficient 
number of times to thoroughly mix them. One of the following 
methods is generally used. (Taylor and Thompson's Concrete.) 

(a) Cement and sand mixed dry and shoveled on the stone or 
gravel, leveled oil', and wet as the mass is turned. 



MASONRY AND REINFORCED CONCRETE 75 

(b) Cement aud sand mixed dry, the stone measured and dumped 
on top of it, leveled off, and wet, as turned with shovels. 

(c) Cement and sand mixed into a mortar, the stone placed on top 
of it and the mass turned. 

(d) Cement and sand mixed with water into a mortar which is 
shoveled on the gravel or stone and the mass turned with shovels. 

(e) Stone or gravel, sand, and cement spread in successive layers, 
mixed slightly and shoveled into a mound, water poured into the center, 
and the mass turned with shovels. 

The quantity of water is regulated by the appearance of the 
concrete. The best method of wetting the concrete is by measur- 
ing the water in pails. This insures a more uniform mixture than 
by spraying the mass with a hose. 

135. Mixing by Machinery. On large contracts the concrete 
is generally mixed by machinery. The economy is not only in the 
mixing itself hut in the appliances introduced in handling the raw 
materials and the mixed concrete. If all materials are delivered 
to the mixer in wheel-barrows, and if the concrete is conveyed away 
in wheel-barrows, the cost of making concrete is high, even if machine 
mixers are used. If the materials are fed from bins by gravity 
into the mixer, and if the concrete is dumped from the mixer into 
cars and hauled away, the cost of making the concrete should be 
very low. On small jobs the cost of maintaining and operating 
the mixer will usually exceed the saving in hand labor and will 
render the expense with the machine greater than without it. 

136. Machine vs. Hand Mixing. It has already been stated 
that good concrete may be produced by either machine or hand mix- 
ing, if it is thoroughly mixed. 

Tests made by the U. S. Government engineers at Duluth, 
Minn., to determine the relative strength of concrete mixed by hand 
and mixed by machine (a cube mixer), showed that at 7 days, hand- 
mixed concrete possessed only 53 per cent of the strength of the 
machine-mixed concrete; at 28 days, 77 per cent; at 6 months, 84 
per cent; and at one year, 88 per cent. Details of these tests are 
given in Table X. 

It should be noted in this connection, that the variations in 
strength from highest to lowest were greatest in the hand-mixed 
samples, and that the strength was more uniform in the machine- 
mixed. 



76 



MASONRY AND REINFORCED CONCRETE 



TABLE X 
Tensile Tests of Concrete 

(From "Concrete and Reinforced Concrete Construction," by H. A. Reid) 



Age, and Method of Mixing 


High 


Low 


Average 


Age 7 Days 
Machine-Mixed Sample 
Hand-Mixed Sample 


260 
159 


243 
113 


253 
134 


Age 28 Days 
Machine-Mixed Sample 
Hand-Mixed Sample 


294 
231 


249 
197 


274 
211 


Age 6 Months 
Machine-Mixed Sample 
Hand-Mixed Sample 


441 
355 


345 

298 


388 
324 


Age One Year 
Machine-Mixed Sample 
Hand-Mixed Sample 


435 
369 


367 
312 


391 
343 



The mixture tested was composed of 1 part cement and 10.18 
parts aggregate. 

STEEL FOR REINFORCING CONCRETE 

137. Steel for reinforcing concrete is not usually subjected to 
so severe treatment as ordinary structural steel, as the impact effect 
is likely to be less; but the quality of the steel should be carefully 
specified. To reduce the cost of reinforced-concrete structures, 
there has been a great tendency to use cheap steel. It has been 
generally recognized in the design of reinforced concrete, that the 
yield point or elastic limit of the steel shall be considered as the failing 
point. It has been shown by beam tests, that when the yield point 
of the steel is reached, the beam sags because of the stretching or 
slipping of the steel, and the top of the beam is likely to crush. 

138. Quality of Reinforcing Steel. The grades of steel used 
in reinforced concrete range from soft to fairly hard. These grades 
of steel may be classified under three heads: soft, medium,*SLnd hard. 

Soft steel should have an ultimate strength of 50,000 to 00,000 
pounds per square inch, and an elastic limit of 28,000 to 35,000 
pounds per square inch. The elongation should be 25 per cent in 8 
inches; and the specimen should bend cold 180 degrees flat on itself, 
without fracture on the outside. 



MASONRY AND REINFORCED CONCRETE 77 

Medium steel, ordinary market steel, has an ultimate strength 
of 60,000 to 70,000 pounds per square inch; and the elastic limit 
ranges from 35,000 to 40,000 pounds per square inch. The elonga- 
tion should be 22 per cent in 8 inches, and the specimen should bend 
cold around a diameter equal to the thickness of the piece tested. 
This steel is manufactured and sold under standard conditions, and 
usually it can safely be used without being tested. 

Hard steel, better known as high-carbon steel, should have an 
ultimate strength of 85,000 to 105,000 pounds per square inch; and 
the elastic limit should be from 50,000 to 65,000 pounds per square 
inch. The elongation should not be less than 10 per cent in 8 inches 
for a test piece | to f inch in diameter. A test piece \ inch in thick- 
ness should bend 100 degrees without fracture, around a diameter 
equal to its own. The high steel has a larger percentage of carbon 
than the medium steel, and therefore the yield point is higher. This 
steel is to be preferred for reinforced-concrete work; but it should 
be thoroughly tested, as many engineers object to it on account of 
its brittleness and the poor quality of the material from which it is 
sometimes rolled. On account of its higher elastic limit, a smaller 
percentage of steel is required ; and when rolled under proper specifi- 
cations and inspection, high steel is more economical for use than 
low-carbon steel. 

In high-carbon steel, the chemical properties should conform 
to the following limits : 

Phosphorus not to exceed 0.06 per cent. 

Sulphur not to exceed 0.0G per cent. 

Manganese not to exceed 0.80 nor less than 0.40 per cent. 

Carbon not to exceed . G5 nor less than . 45 per cent. 

In comparing the two processes of making steel, the products of 
Bessemer steel found in the general market are apt to be extremely 
irregular in their composition, although they may be rolled into like 
forms and sold for the same purpose. Open-hearth products pur- 
chased in the open market and designed to serve the same purpose, 
are more uniform in quality. Test specimens cut from different 
parts of the same Bessemer steel plate, often show a wide difference 
in their mechanical properties. In the open-hearth steel, this wide 
difference is not found, this grade of steel being more homogeneous 
than the Bessemer plates. 



78 MASONRY AND REINFORCED CONCRETE 

139. Types of Reinforcing Steel. The reinforcing steel usually 
consists of small bars of such shape and size that they may easily be 
bent and placed in the concrete so as to form a monolithic structure. 
To distribute the stress in the concrete, and secure the necessary 
bond between the steel and concrete, the steel required must be sup- 
plied in comparatively small sections. All types of the regularly 
rolled small bars of square, round, and rectangular section, as well 
as some of the smaller sections of structural steel, such as angles, 
T-bars, and channels, and also many special rolled bars, have been 
used for reinforcing concrete. These bars vary in size from J inch 
for light construction, up to IV inches for heavy beams, and up to 
2 inches for large columns. In Europe, plain round bars have been 
extensively used for many years; and in the United States also, 
they have been extensively used, but not to the same extent as in 
Europe; that is, in America a very much larger percentage of 
work has been done with deformed bars. 

140. Plain Bars. With plain bars, the transmission of stresses 
is dependent upon the adhesion between the concrete and the steel. 

Square and round bars show about 
the same adhesive strength, but 
the adhesive strength of flat bars 
is far below that of the round and 

Fig. 13. Ransome Twisted Steel Bar. 

square bars. The round bars are 
more convenient to handle and easier obtained, and have, there- 
fore, generally been used when plain bars were desirable. 

141. Structural Steel. Small angles, T-bars, and channels 
have been used to a greater extent in Europe than in this country. 
They are principally used where riveted skeleton work is prepared 
for the steel reinforcement; and in this case, usually, it is desirable 
to have the steel work self-supporting. 

142. Deformed Bars. There are many forms of reinforcing 
materials on the market, differing from one another in the manner of 
forming the irregular projections on their surface. The object of 
all these special forms of bars is to furnish a bond with the concrete, 
independent of adhesion. This bond formed between the deformed 
bar and the concrete, is usually called a mechanical bond. Some of 
the most common types of bars used are the Ransome, Thacher, 
Johnson, Diamond, Kahn, and Twisted Lug. 




MASONRY AND REINFORCED CONCRETE 



79 



The Ransome or twisted bar, shown in Fig. 13, was one of the 
first steel bars shaped to give a mechanical bond with concrete. This 
type of bar is a commerical square bar twisted while cold. There 
are two objects in twisting the bar — first, to give the metal a mechani- 
cal bond with the concrete; second, to increase the elastic limit and 
ultimate strength of the bar. In twisting the bars, usually one 
complete turn is given the bar in eight or nine diameters of the bar, 



■P*f 




Fig. 14. Thacher Patent Bar. 



with the result that the elastic limit of the bar is increased from 40 to 
50 per cent, and the ultimate strength is increased from 25 to 35 per 
cent. These bars can readily be bought already twisted; or, if it 
is desired, square bars may be bought and twisted on the site of the 
work. 

The Thacher bar (Fig, 14) was patented by Mr. Edwin Thacher, 
M. Am. Soc. C. E. These bars are rolled from medium steel, and 
range in size from J inch to 2 inches. The cross-sectional area is 
practically uniform 
throughout, and all 
changes in shape of 
section are made 
by gradual curves. 

The Johnson 
or Corrugated bar 

(Fig. 15), with corrugations on all four sides, was invented by Mr. 
A. L. Johnson, M. Am. Soc. C. E. The corrugations, are so placed 
that the cross-sectional area is the same at all points. The angles 
of the sides of these corrugations or square shoulders, vary from the 
axis of the bars not exceeding the angle of friction between the bar 
and concrete. These bars are usually rolled from high-carbon steel 
having an elastic limit of 55,000 to 65,000 pounds per square inch 
and an ultimate strength of about 100,000 pounds per square inch. 
They are also rolled from any desired quality of steel. In size they 




Fig. 15. Johnson Bar. 



80 



MASONRY AND REINFORCED CONCRETE 



range from J inch to 1J inches, their sectional area being the same 
as that of commercial square bars of the same size. 

The Diamond bar (Fig. 16) was devised by Mr. William Mueser. 
This bar has a uniform cross-section throughout its length, exerts a 




Fig. 16. Diamond Bar. 



uniform bonding strength at every section, and every portion is 
available for tensile strength. In design, this bar consists of a round 
bar with interlacing longitudinal semicircular ribs, and without any 
sharp angles. The Diamond bar is one of the newer types of bars. 




Fig. 17. Kahn Trussed Bar. 



The Kahn bar (Fig. 17) was invented by Mr. Julius Kahn, 
Assoc. M. Am. Soc. C. E. This bar is designed with the assumption 
that the shear members should be rigidly connected to the horizontal 
members. The bar is rolled with a cross-section as shown in the 




Fig. 18. Cold Twisted Lug Bar. 

figure. The thin edges are cut and turned up, and form the shear 
members. These bars are manufactured in several sizes. 

The Twisted Lug bar (Fig. 18) is similar in form to the Ransome 
cold-twisted bar, with the addition of lugs or truncated cones placed 
at regular intervals along the spirals. These bars are rolled with the 
lugs, and the twisting is done either while the bars are hot or at any 




STOPPING THE SLIDING OF A RETAINING WALL, LOUISVILLE, KENTUCKY 

Wall rests on a stratum of clay, plastic when wet, overlying sand and gravel. Its lower 
part is a scries of stone-filled timber cribs, under which, at highest part of wall, wooden piles 
were driven to prevent sliding. Above cribs to street grade, wall is of stone laid dry. Repeated 
floods in creek running parallel with wall, probably rotted piles, allowing wall to slide forward 
under pressure of its earth backing. This was finally stopped by building a retaining wall of 
reinforced concrete, of inverted T shape, on 15-ft. reinforced concrete piles, about 10 ft. in front 
of old wall, the intermediate space filled with earth paved on top with dry block stone to pre- 
vent washing. 

Courtesy of J. P. Claybrook, Chief Engineer, Dept. of Public Works, Louisville, Ky 



MASONRY AND REINFORCED CONCRETE 



81 



time after they are cold. If the* bars are twisted while hot, their 
elastic limit and ultimate strength 'are not raised; that is, their physi- 
cal properties are not changed. 

Expanded metal (Fig. 19) is made from plain sheets of steel, slit 
in regular lines and opened into meshes of any desired size or section 




Fig. 19. Styles of Expanded Metal. 



of strand. It is commercially designated by giving the gauge of the 
steel and the amount of displacement between, the junctions of the 
meshes. The most common manufactured sizes are as follows: 

Standard Sizes of Expanded Metal 



Mesh 


Gauge 


Weight per Sq. Ft. 


Sectional Area 
1 foot wide 


.3-inch 
3 : inch 
6-inch 


No. 16 
No. 10 
No. 4 


.30 lbs. 

.625 lbs. 
.86 lbs. 


.032 sq. in. 
. 177 sq. in. 
.243 sq. in. 



Steel wire fabric reinforcement consists of a netting of heavy and 
light wires, usually with rectangular meshes. The heavy wires 
carry the load, and the light ones are used to space the heavier ones. 
There are many forms of wire fabric on the market. 

Table XI is condensed from the handbook of the Cambria Steel 
Company, and gives the standard weights and areas of plain round 



82 



MASONRY AND REINFORCED CONCRETE 



and square bars as commonly used in reinforced-concrete construc- 
tion : 

TABLE XI 

Weights and Areas of Square and Round Bars 

(One cubic foot of steel weighs 489 . 6 pounds) 





Weight of 


Weight of 








Thickness or 


Square Bar, 


Round Bar, 


Area of 


Area of 


ClRCUM OF 


Diameter 




1 Foot Long 


Square Bar 


Round Bar 


Round Bar 


(Inches) 


(Pounds) 


(Pounds) 


(Sq. In.) 


(Sq. In.) 


(Inches) 


i 


.213 


.167 


.0525 


.0491 


.7854 


A 


.332 


.261 


.0977 


.0767 


.9817 


t 


.478 


.376 


.1406 


.1104 


1.1781 


A 


.651 


.511 


.1914 


.1503 


1.3744 


* 


.850 


.668 


.2500 


.1963 


1 . 5708 


5. 


1.328 


1.043 


.3906 


.3068 


1.9635 


1 


1.913 


1.502 


.5625 


.4418 


2.3562 


1 


3.400 


2.670 


1 . 0000 


.7854 


3.1416 


1* 


4.303 


3.379 


1.2656 


.9940 


3.5343 


H 


5.312 


4.173 


1.5625 


1.2272 


3.9270 


14 


7.650 


6.008 


2 . 2500 


1.7671 


4.7124 


U 


10.41 


8.178 


3.0625 


2.4053 


5.4078 


2 


13.60 


10.68 


4 . 0000 


3.1416 


6.1823 




Rein forced-Concrete Bridge Slabs in Storage Yard of Illinois Central Railway, Chicago. 




Form Box, with Reinforcing Bars, for Construction of Slabs Shown Above. 

CONSTRUCTION OF REINFORCED-CONCRETE BRIDGE SLABS 

Blabs measure 25 ft. by 6 ft. 2 in. by 2 ft. 10 in., reinforced with "Johnson" corrugated bars; 
used on 25-ft. spans for track elevation work. Designed by R. E. Gaut, Bridge Engineer, and 
A. S. Baldwin, Chief Engineer, Illinois Central Railway. 




REINFORCED-CONCRETE ARCH RIB, WALNUT LANE BRIDGE, PHILADELPHIA, PA. 

Courtesy of Geo. £>'. Webster, Chief Engineer \ Bureauoj Surveys, Vept. of Public Works* 



MASONRY AND REINFORCED 
CONCRETE 

PART II 



STONE MASONRY 

14.'3. Definitions. In the following paragraphs, the meanings 
of various technical terms frequently used in stone masonry, are 
clearly explained : 

Arris — The external edge formed by two surfaces, whether 
plane or curved, meeting each other. 

Ashlar — A stone wall built of stones having rectangular faces 
and with joints dressed so closely that "the distance between the 
general planes of the surfaces of the adjoining stones is one-half 
inch or less." 

Ax or Pean Hammer — This tool (Fig. 20) is similar to a double- 
bladed wood-ax. It is used after 
the stone is rough-pointed, to 
make drafts along the edges of £ 
the stone. For rubble work, and 
even for squared-stone work, no 
finer tool need be used. 

Backing — The masonry on the back side of a wall; usually of 
rougher quality than that on the face. 

Batter — The variation from the perpendicular, of a. wall surface. 
It is usually expressed as the ratio of the horizontal distance to the 
vertical height. For example, a batter of 1:12 means that the wall 
has a slope of one inch horizontally to each twelve inches of height. 

Bearing Block — A block of stone set in a wall with the special 
purpose of forming a bearing for a concentrated load (such as the 
load of a beam). 

Bed-Joint — A horizontal joint, or one which is nearly perpendicu- 
lar to the resultant line of pressure (see Joint). 

Copyright, ioo^, by American School of Correspondence 



Fig. 20. Ax or Pean Hammer. 



84 



MASONRY AND REINFORCED CONCRETE 



Belt-Course — A horizontal course of stone extending around one 
or more faces of a building; it is usually composed of larger stones 
which sometimes project slightly, and is usually employed only for 
architectural effect. 

Bonding — A system of arranging the stones so that they are 
mutually tied together by the overlapping of joints. 

Bush-Hammering — A method of finishing by which the surface 
of the stone, after being roughly dressed to a surface which is nearly 



www 
Fig. 21. Bush-Hammer. 








Fig. 23. Cavil. 



V 



o 

V V 



Fig. 22. Buttress. 



Fig. 24. Chisel. 



plane, is smoothed still more with a bush-hammer (see Fig. 21). The 
face of the bush-hammer has a large number of small pyramidal 
points, which, in skilful hands, speedily reduce the surface to a uni- 
formly granular condition. 

Buttress — A very short wall (Fig. 22) built perpendicular to a 
main wall which may be subjected to lateral thrust, in order to re- 
sist by compression the tendency to tip over. (See Counterfort.) 

Cavil — A tool which has one blunt face, and a pyramidal point 
at the other end (Fig. 23). It is used for roughly breaking up stone. 

Chisel — A tool made of a steel bar which has one end forged 
and ground to a chisel edge (Fig. 24). It is used for cutting drafts 
for the edges of stones. 

Coping — A course of stone which caps the top of a wall. 

Corbel — A stone projecting from the face of a wall for the pur- 



MASONRY AND REINFORCED CONCRETE 85 

pose of supporting a beam or an arch which extends out from the 
wall. 

Counterfort — A short wall built behind a retaining wall, to relieve 
by tension the overturning thrust against the wall. (See Buttress.) 

Course — A row of stones of equal height laid horizontally along 
a wall. 

Coursed Masonry — Masonry having courses of equal height 
throughout. 

('onrsnl Rubble— Rubble masonry (see Rubble) which is leveled 
off at certain definite heights so as to make continuous horizontal 
joints. The expediency of this is doubtful. It certainly adds some- 
thing to the cost; it probably makes the wall somewhat weaker, and 
is no advantage either mechanically or in appearance. 

( 'ramp — A bar of iron, the ends of which are bent at right angles, 
which is inserted in holes and grooves specially cut for it in adjacent 
stones in order to bind the stones together. When they are carefully 
packed with cement mortar, they are ef- 
fectively prevented from rusting. 

Crandall — A tool made by fitting a f Hill 11 11 

series of steel points into a handle, using a 
wedge (see Fig. 25), by means of which a 
series of fine picks at the stone are made 
with each stroke, and the surface is more 
quickly reduced to a true plane. 

Crandalling — A system of dressing stone by which the surface, 
after having been rough-pointed to a fairly plane surface, is ham- 
mered with a crandall such as is illustrated in Fig. 25. 

Dimension Stone — Cut stone whose precise dimensions in a 
building are specified in the plans. The term refers to the highest 
grade of ashlar work. 

Dovjel — A straight bar of iron, copper, or even stone, which is 
inserted in two corresponding holes in adjacent stones. They may 
be vertical across horizontal joints, or horizontal across vertical 
joints. In the latter case, they are frequently used to tie the stones 
of a coping or cornice. The extra space between the dowels and the 
stones should be filled with melted lead, sulphur, or cement grout. 

Draft — A line on the surface of a stone which is cut to the breadth 
of the draft chisel. 



11 



86 MASONRY AND REINFORCED CONCRETE 

Dry Stone Masonry — Masonry which is put in place without 
mortar. 

Extrados — The upper surface of an arch. 
Face — The exposed surface of a wall. 

Face-Hammer — A tool having a hammer face and an ax face. 
It is used for roughly squaring up stones, either for rubble work or in 
preparation for finer stone dressing. See 
Fig. 26. 

Feathers — See Plugs. 

Footing — The foundation masonry for a 



Fig. 26. Face-Hammer. Wal1 0f P ier > USUall y Composed (in stone 

masonry) of large stones having a sufficient 
area so that the pressure upon the subsoil shall not exceed a safe limit, 
and having sufficient transverse strength to distribute the pressure 
uniformly over the subsoil. 

Grout— A thin mixture of cement, sand, and water, which is 
sometimes forced by pressure into the cracks in defective masonry 
or to fill cavities which have formed behind masonry walls. Some- 
times grout has been used to solidify quicksand. Its use must always 
be considered as a makeshift with which to improve a bad condition 
of affairs. It is frequently used in the endeavor to hide defective 
work. 

Header — A stone laid with its greatest dimension perpendicular 
to the face of a wall. Its purpose is to bond together the facing and 
the backing. 

Intrados — The inner (or under) surface of an arch. 

Jamb — The vertical sides of an opening left in a wall for a door 
or window. 

Joint — The horizontal and vertical spaces between the stones, 
which are filled with mortar, are called the joints. When they are 
horizontal, they are called bed- joints. Their width or thickness 
depends on the accuracy with which the stones are dressed. The 
joint should always have such a width that any irregularity on the 
surface of a stone shall not penetrate completely through the mortar 
joint and cause the stones to bear directly on each other, thus pro- 
ducing concentrated pressures and transverse stresses which might 
rupture the stones. The criterion used by a committee of the 
American Society of Civil Engineers in classifying different grades of 



MASONRY AND REINFORCED CONCRETE 



87 



masonry, is to make the classification depend on the required thick- 
ness of the joint. These thicknesses have been given when defining 
various grades of stone masonry. 

Lintel — The stone, iron, wood, or concrete beam covering the 
opening left in a wall for a door or window. 

Natural Bed — The surfaces of a stone parallel to its stratifi- 
cation. 

One- Man Stone — A term used to designate roughly the size and 





Pig. -27. Pick. 



Fig. 28. Pitched-Faced Masonry. 



£=\ 



f^ 



V IS 



weight of stone used in a wall. It represents, approximately, the size 
of stone which can be readily and continuously handled by one man. 

Plch — A tool which roughly resembles an earth pick, but which 
has two sharp points. It is used like a cavil for 
roughly breaking up and forming the stones as de- 
sired. (See Fig. 27.) 

Pitched-Faced Masonry — That in which the 
edges of the stone are dressed to form a rectangle 
which lies in a true plane, although the portion of 
the face between the edges is not plane. (See 
Fig. 28.) 

Pitching Chisel — A tool which is used with a 
mallet to prepare pitched-face masonry. The usual dimensions are 
as illustrated in Fig. 29. 

Plinth — Another term for Water-Table, which see. 

Plug — A plug is a truncated wedge (see Fig. 30). Correspond- 
ing with them are wedge-shaped pieces made of half-round malleable 
iron. A plug is used in connection with a pair of feathers to split a 
section of stone uniformly. A row of holes is drilled in a straight 



Fig. 29. 



Pitching 
Chisel. 



88 



MASONRY AND REINFORCED CONCRETE 




line along the surface of the stone, and a plug and pair of feathers 
are inserted in each hole. The plugs in succession are tapped lightly 
with a hammer so that the pressure produced by all the plugs is in- 
creased as uniformly as possible. When the pressure is uniform, the 
stone usually splits along the line of the holes without injury to the 
portions split apart. 

Point — A tool made of a bar of steel whose end is ground to a 
point. It is used in the intermediate stage of dressing an irregular 

surface which has already been 
roughly trued up with a face- 
hammer or an ax. For rough 
masonry, this maybe the finishing 
tool. For higher-grade masonry, 
such work will be followed by 
bush-hammering, crandalling, etc. 
Pointing — A term applied to 
the process of scraping out the 
mortar for a depth of an inch or 
more on the face of a wall after 
the wall is complete and is sup- 
posed to have become compressed 
to its final form; the joints are then filled with a very rich mortar — 
say equal parts of cement and sand. Although ordinary brickwork 
is usually laid by finishing the joints as the work proceeds, it is 
impossible to prevent some settling of the masonry, which usually 
squeezes out some of the mortar and leaves it in a cracked condition 
so that rain can readily penetrate through the cracks into the wall. 
By scraping out the mortar, which may be done with a hook before 
it has become thoroughly hard, the joint may be filled with a high 
grade of mortar which will render it practically impervious to rain- 
water. The pointing may be done with a masons' trowel, although, 
for architectural effect, such work is frequently finished off with 
specially formed tools which will mould the outer face of the mortar 
into some desired form. 

Quarry-Faced Stone — Stone laid in the wall as it comes from 
the quarry. The term usually applies to stones which have such 
regular cleavage planes that even the quarry faces are sufficiently 
regular for use without dressing. 




Fig. 30. Plug and Feathers. 



MASONRY AND REINFORCED CONCRETE 89 

Quoin — A stone placed in the corner of a wall so that it forms a 
header for one face and a stretcher for the other. 

Random — The converse of Coursed Masonry; masonry which is 
not laid in courses. 

Range — Masonry in which each course has the same thickness 
throughout, but the different courses vary in thickness. 

Rip-Rap — Consists of rough stone just as it comes from the 
quarry, which is placed on the surface of an earth embankment. 

Rough-Pointing — Dressing the face of a stone by means of a 
pick, or perhaps a point, until the surface is approximately plane. 
This may be the first stage preliminary to finer dressing of the stones. 

Rubble — Masonry composed of stones as they come from the 
quarry without any dressing other than knocking off any objection- 
able protruding points. The thickness may be quite variable, and 
therefore the joints are usually very thick in places. 

Slope-Wall Masonry — A wall, usually of dry rubble, which is 
built on a sloping bank of earth and supported by it, the object of 
the wall being chiefly to protect the embankment against scour. 

Spalls — Small stones and chips, selected according to their 
approximate fitness, which are placed between the larger, irregular 
stones in rubble masonry in order to avoid in places an excessive 
thickness of the mortar joint. Specifications sometimes definitely 
forbid their use. 

Squared-Stone Masonry — Masonry in which the stones are 
roughly dressed so that at the joints "the distance between the 
general planes of the surface of adjoining stones is one-half inch or 
more." 

Stretcher — A stone which is placed in the wall so that its greatest 
dimension is parallel with the wall. 

String-Course — A course of stone or brick running horizontally 
around a building, whose sole purpose is architectural effect (see 
Belt-Course). 

Template — A wooden form used as a guide in dressing stones to 
some definite shape (see Figs. 33 and 34). 

Tivo-Men Stone — A rather indefinite term applied to a size and 
weight of stone which cannot be readily handled except by two men. 
The term has a significance in planning the masonry work. 

Water-Table — A course of stone which projects slightly from the 



90 MASONRY AND REINFORCED CONCRETE 

face of the wall and which is usually laid at the top of the foundation 
wall. Its function is chiefly architectural, although, as its name 
implies, it is supposed to divert the water which might drain down 
the wall of a building, and to prevent it from following the face of 
the foundation wall. 

Wooden Brick — A block of wood placed in a wall in a situation 
where it will later be convenient to drive nails or screws. Such a 
block is considered preferable to the plan of subsequently drilling a 
hole and inserting a plug of wOod into which the screws or nails may 
be driven, since such a plug may act as a powerful wedge and crack 
the masonry. 

144. Classification of Dressed Stones. Stone masonry is 
classified according to the shape of the stones, and also according 
to the quality and accuracy of the dressing of the joints so that the 
joints may be close. The definitions of these various kinds of stone- 
work have already been given in the previous section, and therefore 
will not be repeated here; but the classification will be repeated in 
the order of the quality and usual relative cost of the work. The 
term ashlar refers, to the rectangular shape of the stone and the 
accuracy of dressing the joints, and may be applied to coursed ashlar, 
range, and even random. The next grade in quality is squared-stone 
masonry, which likewise refers only to the accuracy iii dressing the 
joints. The variations in the coursing of the stones may be the same 
as for ashlar. The term rubble is usually applied to stone masonry 
on which but little work has been done in dressing the stones, al- 
though the cleavage planes may be such that very regular stones 
may be produced with very little work. Rubble masonry usually 
has joints which are very irregular in thickness. In order to reduce 
the amount of clear mortar which otherwise might be necessary in 
places between the stones, small pieces of stone called spcdls are 
placed between the larger stones. Such masonry is evidently largely 
dependent upon the shearing and tensile strength of the mortar and 
is therefore comparatively weak. Random rubble (Fig. 31), which 
has joints that are not in general horizontal or vertical, or even 
approximately so, must be considered as a weak type of masonry. 
In fact the real strength of such walls, which are frequently built 
for architectural effect, depends on the backing to which the facing 
stones are sometimes secured by cramps. 




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w 

CO 
CJ 

o 

3 | 

* B 

ai 

< 2 
o a 

CQ - 

fe 5 
o & 

O b£ 




_ — » 

8* 

Or, 

11 






o >* 



MASONRY AND REINFORCED CONCRETE 



91 




Fig. 31. Random Rubble. 



145. Stone Cutting and Dressing. Many of the requirements 
and methods of stone dressing have already been stated in the defi- 
nitions given above. Frequently a rock is so stratified that it can be 
split up into blocks whose faces are so nearly parallel and perpendicu- 
lar that they may be used with little or no dressing in building a sub- 
stantial wall with comparatively 
close joints. On the other hand, 
an igneous rock such as granite 
must be dressed to a regular form. 
The first step in making 
rectangular blocks from any stone 
is to decide from its stratification, 
if any, or its cleavage planes, how 
the stone may be dressed with the 
least labor in cutting. The stone 
is then marked in straight lines 
with some form of marking chalk, and drafts are cut with a 
drafting chisel so as to give a rectangle whose four lines lie all in 
one plane. The other faces are then dressed off with as great 
accuracy as is desired, so that they are perpendicular (or parallel) 
to this plane. For squared-stone masonry, and especially for 
ashlar masonry, the drafts should be cut for 
the bed-joints, and the surface between the 
drafts on any face should be worked down to 
a true plane, or nearly so. The bed-joints 
should be made slightly concave rather than 
convex, but the concavity should be very 
z^^^-^")/ / slight. If the surface is very convex, there 

:::: ^-/{ _J is danger that the stones will come in con- 
tact with each other and produce a concen- 
tration of pressure, unless the joints are 
made undesirably thick. If they are very 
concave, there is a danger of developing 
transverse stresses in the stones, which might cause a rupture. 
The engineer or contractor must be careful to see that the bed- 
joints are made truly perpendicular to the face. A frequent trick 
of masons is to make the stones like truncated wedges, as illus- 
trated in Fig. 32. Such masonry, when finished, may look almost 




Fig. 32. Defective Work. 



92 



MASONRY AND REINFORCED CONCRETE 



like ashlar; but such a wall is evidently very weak, even danger- 
ously so. 

To produce a cylindrical surface on a stone, a draft must be cut 
along the stone, which shall be parallel with the axis of the cylinder. 
See Fig. 33. A template made with a curve of the desired radius, 
and with a guide which runs along the draft, may be used in cutting 
down the stone to the required cylindrical form. A circular template 
swung around a point which may be considered as a pole, may be 
used for making spherical surfaces, although such work is now usually 
done in a lathe instead of by hand. 

To make a warped surface or helicoidal surface, a template must 
be made, as in Fig. 34, by first cutting two drafts which shall fit a 



Template 




Fig. 33. Cylindrical Surface. 



Fig. 34. Template for Warped- Surface 

Cutting. 



template made as shown in the figure. After these two drafts are 
cut, the surface between them is dressed down to fit a straight edge, 
which is moved along the two drafts and perpendicular to them. 
Such stonework is very unusual, and almost its only application is 
in the making of oblique or helicoidal arches. 

The size of the blocks has a very great influence on the cost of 
dressing the stones per cubic yard of masonry. For example, to 
quote a very simple case, a stone 3 feet long, 2 feet wide, and 18 
inches high has 12 square feet of bed-joints, 6 square feet of end joints, 
and 4.5 square feet of facing, and contains 9 cubic feet of masonry. 
If the stones are 18 inches long, 1 foot wide, and 9 inches high (just 
one-half of each dimension), the area of each kind of dressed joint is 
one-fourth that in the case of the larger stones, but the volume of the 
masonry is only one-eighth. In other words, for stones of similar 



MASONRY AND REINFORCED CONCRETE 93 

shape, increasing the size increases the area of dressing in proportion 
to the square of the dimensions, but it also increases the volume in 
proportion to the cube of the dimensions. Therefore large stones are 
far more economical than small stones, so far as the cost of dressing 
is a factor. 

The size of stones, the thickness of courses, and the type of 
masonry should depend largely on the product of the quarry to be 
utilized. An unstratified stone like granite must have all faces of 
the stone plug-and-feathered; and therefore the larger the stone, the 
less will be the area to be dressed per cubic foot or yard of masonry. 
On the other hand, the size of blocks which can be broken out from 
a quarry of stratified rock, such as sandstone or limestone, is usually 
fixed somewhat definitely by the character of the quarry itself. The 
stratification reduces very greatly the work required, especially on 
the bed-joints. But since the stratification varies, even in any one 
cjuarrv, it is generally most economical to use a stratified stone for 
random masonry, while granite can be cut for coursed masonry at 
practically the same expense as for stones of variable thickness. 

146. Cost of Dressing Stone. Although, as explained above, 
the cost of dressing stone should properly be estimated by the square 
foot of surface dressed, most figures which are obtainable give the 
cost per cubic yard of masonry, which practically means that the 
figures are applicable only to stones of the average size used in that 
work. A few figures are here quoted from Gillette's "Handbook of 
Cost Data:" 

(a) Hand Dressing — Wages, 50 cents per hour. Soft, 25 to 30 
cents; medium, 40 to 45 cents; hard, 75 to 80 cents, per square 
foot of surface dressed. 

(b) Hand Dressing — Wages, $3 per day. Limestone, bush-ham- 
mered, 25 cents per square foot. 

(c) Hand Dressing Limestone — 36 square feet of beds and joints 
per 9-hour day (or 4 square feet per hour) ; wages, 40 cents per 
hour, or 10 cents per square foot. 

(d) Hand Dressing Granite — For ^-inch joints, 2G cents per square 
foot. 

(e) Sawing Slabs by Machinery — Costs approximately 17 cents per 
square foot. 

147. Constructive Features — Bonding. It is a fundamental 
principle of masonry construction, that vertical joints (either longi- 
tudinal or lateral) should not be continuous for any great distance. 



94 MASONRY AND REINFORCED CONCRETE 

Masonry walls (except those of concrete blocks) are seldom or never 
constructed entirely of single blocks which extend clear through the 
wall. The wall is essentially a double wall which is frequently con- 
nected by headers. These break up the continuity of the longitu- 
dinal vertical joints. The continuity of the lateral vertical joints is 
broken up by placing the stones of an upper course over the joints in 
the course below. Since the headers are made of the same quality of 
stone (or brick) as the face masonry, while the backing is of com- 
paratively inferior quality, it costs more to put in numerous headers, 
although strength is sacrificed by neglect to do so. For the best 
work, stretchers and headers should alternate. This would usually 
mean that about one-third of the face area would consist of headers. 
One-fourth or one-fifth is a more usual ratio. Cramps and dowels 
are merely devices to obtain a more efficient bonding. An inspector 
must guard against the use of blind headers, which are short blocks of 
stone (or brick), which have the same external appearance on the 
finished wall, but which furnish no bond. After an upper course has 
been laid, it is almost impossible to detect them. 

Amount of Mortar. For the same reasons given when dis- 
cussing the relation of size of stones to amount of dressing required, 
more mortar per cubic yard of masonry is needed for small stones than 
for large. The larger and rougher joints, of course, require more 
mortar per cubic yard of masonry. In the tabular form at top of 
page 95, are given figures which, for the above reasons, are necessarily 
approximate; the larger amounts of mortar represent the require- 
ments for the smaller sizes of stone, and vice versa: 

The stones should be very thoroughly wetted before laying in 
the wall, so that they will not absorb the water in the mortar and 
ruin it before it can set. It is very important that the bed-joints 
should be thoroughly flushed with mortar. All vertical joints should 
likewise be tightly filled with mortar. 

148. Allowable Unit-Pressures. In estimating such quantities, 
the following considerations must be kept in mind : 

(a) The accuracy of the dressing of the stone, particularly the bed- 
joints, has a very great influence. 

(6) The strength is largely dependent on that of the mortar, 
(c) The strength is so little dependent on that of the stone itself that 
the strength of the stone cannot be considered a guide to the strength of 
the masonry. For example, masonry has been known to fail under a load not 



MASONRY AND REINFORCED CONCRETE 95 



Mortar per Cubic Yard of Masonry 



Grade of Masonry 



Ashlar 

Squared-Stone 

Rubble 



Volume of Mortar per Cubic Yard of Masoni 



1 to 2 cubic feet 
4.5 to 7 " 
5.5 to 9 " 



more than five per cent of the ultimate crushing strength of the stone itself. 

(d) The strength of a miniature or small-scale prism of masonry is 
evidently no guide to the strength of large prisms. The ultimate strength of 
these is beyond the capacity of testing machines. 

(e) So much depends on the workmanship, that in any structure 
where the unit-stresses are so great as to raise any question concerning the 
strength, the best workmanship must be required. 

Judging from the computed pressures now carried by noted 
structures, and also from the pressures sustained by piers, etc., which 
have shown distress and have been removed, it is evident that, as- 
suming good workmanship, we may depend on masonry as follows: 

Allowable Pressures on Masonry 

Granite Ashlar up to 400 pounds per sq. inch 

Limestone or Sandstone Ashlar " " ,'300 " 

Squared Stone " " 250 " " " " 

Rubble " " 100 " " " " 

It is interesting to note that, although concrete has been con- 
sit hied inferior even to rubble, unit-stresses of 400 pounds per square 
inch are now being freely employed for concrete. 

149. Cost of Stone Masonry. The total cost is a combination 
of several very variable items as follows: 

1. Value of quarry privilege; 

2. Cost of stripping superincumbent earth or disintegrated rock; 

3. Cost of quarrying; 

4. Cost of dressing; 

5. Cost of transportation (teaming, railroad, etc.) from quarry to 

site of work; 

6. Cost of mortal-; 

7. Cost of centering, scaffolding, derricks, etc.; 

8. Cost of laying; 

9. Interest and depreciation on plant; 
10. Superintendence. 

Some of the above items may be practically nothing, in cases. 
The cost of some of the items has already been discussed. The cost 



96 



MASONRY AND REINFORCED CONCRETE 



of many items is so dependent on local conditions and prices that the 
quotation of the. cost of definite jobs would have but little value and 
might even "be deceptive. The following very general values may be 
useful to give a broad idea of the cost: 

Cost of Stone Masonry 

Rubble Masonry in Mortar $3 .00 to $ 5.00 per cubic yard. 

Squared-Stone Masonry 6.00 to 10.00 " " 

Dimension Stone, Granite Ashlar up to 60.00 " " 

BRICK MASONRY 

Many of the terms employed in stone masonry, and of the 
directions for properly doing the work, are equally applicable to 



1 1 


1 1 II 


□ ^ zzo 


1 1 w 


1 I 



Fig. 35. Common Bond. 

brick masonry, ana therefore will not be here repeated. The follow- 
ing sections will be devoted to those terms and specifications which 
are applicable only to brick masonry. 

150. Bonding Used in Brick Masonry. Some of the principles 
involved in the effect of bonding on the strength of a wall, have al- 
ready been discussed under "Stone Masonry." The other considera- 
tion is that of architectural appearance. The common method of 
bonding (Fig. 35) is to lay five or six courses of brick entirely as 
stretchers, then a course of brick will be laid entirely as headers. 
There is probably some economy in the work required of a brick- 
layer in following this policy. The so-called English Bond (Fig. 36) 
consists of alternate courses of headers and stretchers. If the face 
bricks arc of better quality than those used in the backing of the wall, 
this system means thai one-half the face 4 area of the wall consists of 
headers; which is certainly not an economical way of using the facing 
brick. The Flemish Bond (Fig. 37) employs alternate headers and 



MASONRY AND REINFORCED CONCRETE 



97 



stretchers in each course, and also disposes of the vertical joints so 
that there is a definite pattern in the joints, which has a pleasing 
architectural effect. 

151. Constructive Features. On account of the comparatively 
high absorptive power of brick, it is especially necessary that they 
shall be thoroughly soaked with water before being laid in the wall. 



□CZ -HZ!-,- ~r 


QC 


ZEZ -r- 


III 


nr~ 



Fig. 36. English Bond. 

An excess of water can do no harm, and will further insure the bricks 
being clean from dust, which would affect the adhesion of the mortar. 
It is also important that the brick shall be laid with what is called a 
shove joint. This term is even put in specifications, and has a definite 
meaning to masons. It means that after laying the mortar for the 
bed-joints, a brick is placed with its edge projecting somewhat over 



III 


1 1 1 


1 1 


1 1 


II 


! 1 


1 1 


I 1 


II 


1 



Fig. 37. Flemish Bond. 

that of the lower brick, and is then pressed oown into the mortar, 
and, while still being pressed down, is shoved into its proper position. 
In this way is obtained a proper adhesion between the mortar and the 
brick. 

The thickness of the mortar joint should not be over one-half 
inch; one-fourth inch, or even less, is far better, since it gives stronger 
masonry. It requires more care to make thin joints than thick 



98 MASONRY AND REINFORCED CONCRETE 

joints, and therefore it is very difficult to obtain thin joints when 
masons are paid by piecework. Pressed brick fronts are laid with 
joints of one-eighth inch or even less, but this is considered high- 
grade work and is paid for accordingly. 

152. Strength of Brickwork. As previously stated with respect 
to stone masonry, the strength of brick masonry is largely dependent 
upon the strength of the mortar; but, unlike stone masonry, the 
strength of brick masonry is, in a much larger proportion, dependent 
on the strength of the brick composing it. The ultimate strength of 
brick masonry has been determined by a series of tests, to vary from 
1,000 to 2,000 pounds per square inch, using lime mortar; and from 
1,500 to 3,000 pounds per square inch, using cement mortar — the 
variation in each group (for the same kind of mortar) depending on 
the quality of the brick. A large factor of safety, perhaps 10, should 
be used with such figures. 

153. Methods of Measuring Brickwork. There is unfortunate- 
ly a considerable variation in the methods of measuring brickwork, 
the variation depending on local trade customs. Brickwork is often 
paid for by the perch. The volume of a perch was originally taken 
from a similar volume of stone masonry, the unit being a section of 
the wall one rod (16J feet) long and one foot high. Since the usual 
custom made such a wall 18 inches thick, the volume 24f cubic feet 
came to be considered as one perch of masonry; then this number 
was modified to the round number 25 cubic feet, for convenience of 
computation. The construction of walls one foot thick and with the 
same face unit of measurement, gave rise to a unit volume of 16^ 
cubic feet, which was also called a perch. Such units have un- 
doubtedly arisen from the fact that it requires more work per cubic 
yard to build a thin wall than a thick wall, and the brick mason 
desires a unit of measurement more nearly in accordance with the 
labor involved. 

Brick is- generally paid for by the cubic yard or by the thousand, 
and the bidder must make his own allowance, if necessary, for any 
extra work due to thin walls. The number of brick per cubic yard 
depends on the thickness of the joints and on the size of the bricks. 
A very slight variation in the thickness of the joint will change very 
materially the number of brick per cubic yard, and also the amount of 
mortar. The exact values (according to the size of the brick and the 



MASONRY AND REINFORCED CONCRETE 



99 



thickness of the mortar joint) are as given below; but the values are 
not closely to be depended on, because of these variations: 
Quantities of Brick and Mortar 





Size 
(Inches) 


Thick- 
ness OF 
Joints 


No. of 

Brick 

per Cubic 

Yard 


Mortar 


Kind of Brick 


Per Cubic 
Yard of 
Masonry 


Per 1,000 
Brick 


Common brick 
Pressed " 


81 X 4 X 2{ 
81 X 4 X 21 
8f X 41 X 21 


£ in. 
Jin. 

£ in. 


430 
516 
544 


.34 cu. yd. 
2i « « 

.11 " " 


.SO cu. yd. 
.40 " " 
.21 " " 



It is very common and convenient to estimate that 1,000 brick 
will make two cubic yards of masonry. The number of brick per 
cubic yard given above is the equivalent of 16, 19, and 20 brick per 
cubic foot. Bricklayers (backed up by their unions) sometimes de- 
mand pay per 1,000 brick laid, but compute the number on the basis 
of 7h bricks per superficial foot of a wall 4 inches thick, 15 bricks for 
a "9-inch wall," and 22J bricks for a "13-inch wall." The number 
actually used in a 13-inch wall varies from 17 to 20. 

154. Cost of Brickwork. A laborer should handle 2,000 brick 
per hour in loading them from a car to a wagon. If they are not un- 
loaded by dumping, it will require as much time again to unload them. 
A mason should lay from 1 ,200 to 1 ,500 brick per 9-hour day on 
ordinary wall work. For large, massive foundation work with thick 
walls, the number should rise to 3,000 per day. On the other hand, 
the number may drop to 200 or 300 on the best grade of pressed- 
brick work. About one helper is required for each mason. Masons' 
wages vary from 40 to 60 cents per hour; helpers' wages are about 
one-half as much. 

155. Impermeability. As previously stated, brick is very 
porous; ordinary cement mortar is not water-tight; and therefore, 
when it is desirable to make brick masonry impervious to water, 
some special method must be adopted as described in Part I, under 
the head of "Waterproofing." 

L56. Efflorescence. This name is applied to the white deposit 
which frequently forms on brickwork and concrete, and has already 
been described in Part I. The Sylvester wash has frequently been 
used as a preventive, and with fairly good results. Diluted acid 



(1) 



100 MASONRY AND REINFORCED CONCRETE 

has been used successfully to remove the efflorescence. These 
methods have already been described in Part I. 

157. Brick Piers. A brick pier, as a general rule, is the only 
form of brickwork that is subjected to its full resistance. Sections 
of walls under bearing plates also receive a comparatively large load ; 
but only a few courses receive the full load, and therefore a greater 
unit-stress may be allowed than for piers. 

Kidder gives the following formulae for the safe strength of brick 
piers exceeding 6 diameters in height : 
Piers laid with rich lime mortar, 

TT 

Safe load in pounds per square inch = 110 — 5-=-...(l) 
Piers laid with 1 to 2 Natural cement mortar, 

TT 

Safe load in pounds per square inch = 140 — 5%-pT ' ■ ^ 
Piers laid with 1 to 3 Portland cement mortar, 

TT 

Safe load in pounds per square inch = 200 — 6-~- . . (3) 

In the above formulae, H is the height of the column in feet, and D is 
the diameter of the column in feet. 

For example, a column 16 feet in height and If feet square, laid 
with rich lime mortar, may be subjected to a load of 65 pounds per 
square inch, or 9,360 pounds per square foot; for a 1 to 2 natural 
cement mortar, 90 pounds per square inch, or 12,960 pounds per 
square foot; and for a 1 to 3 Portland cement mortar, 146 pounds per 
square inch, or 20,914 pounds per square foot. 

The building laws of some cities require a bonding stone spaced 
every 3 to 4 feet, when brick piers are used. This stone is 5 to 8 
inches thick, and is the full size of the pier. Engineers and archi- 
tects are divided in their opinion as to the results obtained by using 
the bonding stone. 

CONCRETE 

158. Concrete is extensively used for constructing the many 
different types of foundations, retaining walls, dams, culverts, etc. 
The ingredients of which concrete is made, the proportioning and 
the methods of mixing these materials, etc., have been discussed in 
Part I. Methods of mixing and handling concrete by machinery 
will be discussed in Part IV. Various details of the use of concrete in 
tiie construction of foundations, etc., will be discussed during the 
treatment of the several kinds of work. 



MASONRY AND REINFORCED CONCRETE 101 



RUBBLE CONCRETE 

159. Rubble concrete includes any class of concrete in which 
large stones are placed. The chief use of this concrete is in con- 
structing dams, lock walls, breakwaters, retaining walls, and bridge 
piers. 

The cost of rubble concrete in large masses should be less than 
that of ordinary concrete, as the expense of crushing the stone used 
as rubble is saved, and each large stone replaces a portion of cement 
and aggregate; therefore this portion of cement is saved, as well as 
the labor of mixing it. The weight of a cubic foot of stone is greater 
than that of an equal amount of ordinary concrete, because of the 
pores in the concrete; the rubble concrete is therefore heavier, which 
increases its value for certain classes of work. In comparing rubble 
concrete with rubble masonry, the former is usually found cheaper 
because it requires very little skilled labor. For walls 3 or 31 feet 
thick, the rubble masonry will usually be cheaper, owing to the 
saving in forms. 

160. Proportion and Size of Stone. Usually the proportion of 
rubble stone is expressed in percentage of the finished work. This 
percentage varies from 20 to 65 per cent. The percentage depends 
largely on the size of the stone used, as there must be nearly as much 
space left between small stones as between large ones. The per- 
centage therefore increases with the size of the stones. When "one- 
man" or "two-men" rubble stone is used, about 20 per cent to 25 
per cent of the finished work is composed of these stones. When 
the stones are large enough to be handled with a derrick, the pro- 
portion is increased to about 33 per cent; and to 55 per cent, or even 
65 per cent, when the rubble stones average from 1 to 2\ cubic yards 
each. 

The distance between the stones may vary from 3 inches to 15 or 
18 inches. With a very wet mixture of concrete, which is generally 
used, the stones can be placed much closer than if a dry mixture is 
used. With the latter mixture, the space must be sufficient to allow 
of the concrete being thoroughly rammed into all of the crevices. 
Specifications often state that no rubble stone shall be placed nearer 
the surface of the concrete than 6 to 12 inches. 

161. Rubble Masonry Faces. The faces of dams are very often 



102 MASONRY AND REINFORCED CONCRETE 

built of rubble, ashlar, or cut stone, and the filling between the faces 
made of rubble concrete. For this style of construction, no forms are 
required. For rubble concrete, when the faces are not constructed 
of stone, wooden forms are constructed as for ordinary concrete. 

162. Comparison of Quantities of Materials. The mixture of 
concrete used for this class of work is often 1 part Portland cement, 
3 parts sand., and 6 parts stone. The quantities of materials re- 
quired for one yard of concrete, according to Table VI, are 1.05 
bbls. cement, 0.44 cu. yd. sand, and 0.88 cu. yd. stone. If rubble 
concrete is used, and if the rubble stone laid averages 0.40 cubic 
yard for each yard of concrete, then 40 per cent of the cubic contents 
is rubble, and each of the other materials may be reduced 40 per cent. 
Reducing these quantities gives 1 .05 X 0.60 = 0.63 bbl. of cement; 
0.44 X 0.60 = 0.26 cu. yd. sand; and 0.88 X 0.60 - 0.53 cu. yd. 
of stone, per cubic yard of rubble concrete. 

The construction of a dam on the Quinebaug river is a good 
example of rubble concrete. The height of the dam varies from 30 
to 45 feet above bed-rock. The materials composing the concrete 
consist of bank sand and gravel excavated from the bars in the bed 
of the river. The rock and boulders were taken from the site of the 
dam, and were of varying sizes. Stones containing 2 to 2h cubic 
yards were used in the bottom of the dam, but in the upper part of the 
dam smaller stones were used. The total amount of concrete used 
in the dam was about 12,000 cubic yards. There was \\ cubic 
yards of concrete for each barrel of cement used. The concrete was 
mixed wet, and the large stones were so placed that no voids or 
hollows would exist in the finished work. 

DEPOSITING CONCRETE UNDER WATER 

163. Methods. In depositing concrete under water, some 
means must be taken to prevent the separation of the materials 
while passing through the water. The three principal methods are 
as follows: 

(1) By moans of closed buckets: 
vl) By means of cloth or paper bags; 
(.'•{) By means of t uhes. 

164. Buckets. For depositing concrete by the first method, 
special buckets are made with a closed top and hinged bottom. 



MASONRY AND REINFORCED CONCRETE 103 



Concrete deposited under water must be disturbed as little as pos- 
sible, and in tipping a bucket the material is apt to be disturbed. 
Several different types of buckets with hinged bottoms have been 
devised to open automatically when the place for depositing the con- 
crete has been reached. In one type, the latches which fasten the 
trap doors are released by the slackening of the rope when the bucket 
reaches the bottom, and the doors are open as soon as the bucket 
begins to ascend. In another type, in which the handle extends 
down the sides of the bucket to the bottom, the doors are opened 
by the handles sliding down when the bucket reaches the bottom. 
The doors are hinged to the sides of the bucket, and when opened 
permit the concrete to be deposited in one mass. In depositing 
concrete by this means, it is found rather difficult to place the layers 
uniformly and to prevent the formation of mounds. 

165. Bags. This method of depositing concrete under water 
is by means of open, woven bags or paper bags, two-thirds to three- 
quarters filled. The bags are sunk in the water and placed in courses, 
if possible, header and stretcher system, arranging each course as laid. 
The bagging is close enough to keep the cement from washing out, 
and at the same time, open enough to allow the whole to unite into 
a compact mass. The fact that the bags are crushed into irregular 
shapes which fit into each other, tends to lock them together in a 
way which makes even an imperfect joint very effective. When the 
concrete is deposited in paper bags, the water quickly soaks the 
paper; but the paper retains its strength long enough so that the 
concrete can be deposited properly. 

166. Tubes. The third method of depositing concrete under 
water is by means of long tubes, 4 to 14 inches in diameter. The 
tubes extend from the surface of the water to the place where the 
concrete is to be deposited. If the tube is small, 4 to 6 inches in 
diameter, a cap is placed over the bottom, the tube filled with con- 
crete, and lowered to the bottom. The cap is then withdrawn; and 
as fast as the concrete drops out of the bottom, more concrete is put 
in at the top of the tube, and there is thus a continuous stream of 
concrete deposited. 

When a large tube is used to deposit concrete in this manner, 
it will be too heavy to handle conveniently if filled before being 
lowered. The foot of the tube is lowered to the bottom, and the 



104 MASONRY AND REINFORCED CONCRETE 

water rises into the chute to the same level as that outside; and into 
this water the concrete must be dumped until the water is wholly 
replaced or absorbed by the concrete. This has a tendency to separate 
the cement from the sand and gravel, and will take a yard or more 
concrete to displace the water in the chute. There is a danger that 
this amount of badly washed concrete will be deposited whenever it 
is necessary to charge the chute. This danger occurs not only when 
the charge is accidentally lost, but whenever the work is begun in the 
morning or at any other time. Whenever the work is stopped, the 
charge must be allowed to run out, or it would set in the tube. The 
tubes are usually charged by means of wheelbarrows, and a continu- 
ous flow of concrete must be maintained. When the chute has been 
filled, it is raised slowly from the bottom, allowing a part of the con- 
crete to run out in a conical heap at the foot. 

This method has also been used for grouting stone. In this 
case, a 2-inch pipe, perforated at the bottom, was used. The grout, 
on account of its great specific gravity, is sufficient to replace the 
water in the interstices between the stones, and firmly cement them 
into a mass of concrete. A mixture of one part cement and one part 
sand is the leanest mixture than can be used for this purpose, as 
there is a great tendency for the cement and sand to separate. 

CLAY PUDDLE 

Clay puddle consists of clay and sand made into a plastic mass 
with water. It is used principally to fill cofferdams, and for making 
embankments and reservoirs water-tight. 

167. Quality of Clay. Opaque clays with a dull earthy fracture, 
of an argillaceous nature, which are greasy to the touch, and which 
readily form a plastic paste when mixed with water, are the best clays 
for making puddle. Large stones should be removed from the clay, 
and it should also be free from vegetable matter. Sufficient sand 
and water should be added to make a homogeneous mass. If too 
much sand is used, the puddle will be permeable; and if too little is 
used, the puddle will crack by shrinkage in drying. It is very import- 
ant that clay for making puddle should show great cohesive power 
and also the property of retaining water. 

A simple test to find the cohesive property, can easily be made. 
A small quantity of the clay is mixed with water and made into a roll 



MASONRY AND REINFORCED CONCRETE 105 

about 1 inch in diameter and 8 to 10 inches long; and if, on being 
suspended by one end while wet, it does not break, the cohesive 
strength is ample. The test to find its water-retaining properties 
is made by mixing up 1 or 2 cubic yards of the clay w T ith water, making 
it into a homogeneous plastic mass. A round hole is made in the 
top of the mass, large enough to hold 4 or 5 gallons of water. The 
hole is filled with water, and the top covered and left 24 hours; when 
the cover is removed, the properties of the clay will be indicated by 
the presence or absence of water. 

1GS. Puddling. The clay should be spread in layers about 3 
inches thick and well chopped with spades, aided by the addition of 
sufficient water to reduce it to a pasty condition. Water should be 
given a chance to pass through freely as the clay is being mixed. The 
different layers, as they are mixed, should be bonded together by 
the spade passing through the upper layer into the under layer. The 
test for thorough puddling is that the spade will pass through the 
layer with ease, which it will not do if there are any hard lumps. 

When a large amount of puddle is required, harrows are some- 
times used instead of spades. Each layer of clay is thoroughly har- 
rowed, aided by being sprinkled freely with water, and is then rolled 
with a grooved roller to compact it. 

Puddle, when finished, should not be exposed to the drying 
action of the air, but covered with dry clay or sand. 

FOUNDATIONS 

169. It would be impossible to over-emphasize the importance 
of foundations, because the very fact that the foundations are under- 
ground and out of sight detracts from the consideration that many 
will give to the subject. It is probably true that a yielding of the 
subsoil is responsible for a very large proportion of the structural 
failures which have occurred. It is also true that many failures of 
masonry, especially those of arches, are considered as failures of the 
superstructure, because of breaks occurring in the masonry of the 
superstructure, which have really been due, however, to a settlement 
of the foundations, resulting in unexpected stresses in the super- 
structure. It is also true that the design of foundations is one which 
calls for the exercise of experience and broad judgment, to be able 
to interpret correctly such indications as are obtainable as to the real 



106 MASONRY AND REINFORCED CONCRETE 

character of the subsoil and its probable resistance to concentrated 
pressure. 

170. Classification of Subsoil. The character of soil on which 
it may be desired to place a structure, varies all the way from the 
most solid rock to that of semi-fluid soils whose density is but little 
greater than that of water. The gradation between these extremes 
is so uniform that it is practically impossible to draw a definite line 
between any two grades. It is convenient, however, to group sub- 
soils into three classes, the classification being based on the method 
used in making the foundation. These three classes of subsoils are: 
(a) Firm-, (b) Compressible; and (c) Semi-fluid. 

(a) Firm Subsoils. These comprise all soils which are so 
firm, at least at some reasonably convenient depth, that no treatment 
of the subsoil or any other special method needs to be adopted to 
obtain a sufficiently firm foundation. This, of course, practically 
means that the soil is so firm that it can safely withstand the desired 
unit-pressure. It also means that a soil which might be classed as 
firm soil for a light building should be classed as compressible soil 
for a much heavier building. It frequently happens that the top 
layers must be removed from rock because the surface rock has 
become disintegrated by exposure to the atmosphere. Nothing 
further needs to be done to a subsoil of this kind. 

(6) Compressible Subsoils. These include soils which might be 
considered as firm soils for light buildings such as dwelling-houses, 
but which could not withstand the concentrated pressure that 
would be produced, for example, by the piers or abutments of a 
bridge. Such soils may be made sufficiently firm by methods de- 
scribed later. 

(c) Semi-Fluid Subsoils. These are soils such as are frequently 
found on the banks or in the beds of rivers, which are so soft that 
they cannot sustain without settlement even the load of a house, to 
say nothing of a heavier structure. Nor can they be materially 
improved by any reasonable method of compression. The only 
possible method of placing a heavy structure in such a locality, 
consists in sinking some sort of a foundation through such soft soil 
until it reaches and is supported by a firm soil or by rock, which may 
be 50 or even 100 feet below the surface. The general methods of 
accomplishing these results will be detailed in the following sections. 




( H 



2 -a 

5 § 



JJ o 

:> 

o 

» § 

s a 

w . 

> 2 




Reinforced-Concrete Arch Culvert, Completed. 




Forms for Construction of Arched Culvert Shown Above. 
VIEWS OF CONSTRUCTION ON LINE OF ILLINOIS AND MISSISSIPPI CANAL 



MASONRY AND REINFORCED CONCRETE 107 

171. Testing the Bearing Power. The first step is to excavate 
the surface soil to the depth at which it would be convenient to place 
the foundation and at which the soil appears, from .mere inspection, 
to be sufficiently firm for the purpose. An examination of the 
trenches or foundation pits with a post-auger or steel bar will generally 
be sufficient to determine the nature of the soil for any ordinary 
building. The depth to which such an examination can be made 
with a post-auger or steel bar will depend on the nature of the soil. 
In ordinary soils there will not be much difficulty in extending such an 
examination 3 to 6 feet below the bottom of the foundation pits. In 
common soils or clay, borings 40 feet deep (or even deeper) can readily 
be made with a common wood-auger, turned by men. From the 
samples brought up by the auger, the nature of the soil can be deter- 
mined; but nothing of the compactness of the soil can be determined 
in this manner. 

In order to test a soil to find its compressive value, the bottom 
of the pit should be leveled for a considerable area, and stakes should 
be driven at short intervals in each direction. The elevations of the 
tops of all the stakes should be very accurately taken with a spirit 
level. For convenience, all stakes should be driven to the same level. 
A mast whose base has an area one foot square can support a plat- 
form which may be loaded with several tons of building material, 
such as stone, brick, steel, etc. This load can be balanced with 
sufficient closeness so that some very light guys will maintain the 
unstable equilibrium of the platform. As the load on the platform 
is greatly increased, at some stage it will be noted that the mast and 
platform have begun to sink slightly, and also that the soil in a circle 
around the base of the mast has begun to rise. This is indicated 
by the rising of the tops of the stakes. Even a very ordinary soil 
may require a load of five or six tons on a square foot before any 
yielding will be observable. One advantage of this method lies in 
the fact that the larger the area of the foundation, the greater will be 
the load per square foot which may be safely carried, and that the 
uncertainty of the result is on the safe side. A soil which might 
yield under a load concentrated on a mast one foot square, would 
probably be safe under that same unit-load on a continuous footing 
which was perhaps three feet wide; and if, in addition, a factor of 
safety of three or four was used, there would probably be no question 



108 MASONRY AND REINFORCED CONCRETE 

as to the safety. Such a test need be applied only to an earthy soil. 
It would be practically impossible to produce a yielding by such a 
method on any kind of rock or even on a compacted gravel. 

172. Bearing Power of Ordinary Soils. A distinction must be 
maintained between the crushing strength of a cube of rock or soil, 
and the bearing power of that soil when it lies as a mass of indefinite 
extent under some structure. A soil can fail only by being actually 
displaced by the load above it, or because it has been undermined, 
perhaps by a stream of water. A sample of rock which might crush 
with comparative ease when tested as a six-inch cube in a testing 
machine, will probably withstand as great a concentration of load 
as it is practicable to put upon it by any engineering structure. Even 
a gravel which would have absolutely no strength if it were attempted 
to place a cube of it in a testing machine, will be practically 
immovable when lying in a pit where it is confined laterally in all 
directions. 

173. Rock. The ultimate crushing strength of stone varies 
greatly. The crushing strength is usually determined by making 
tests on small cubes. Tests made on prisms of a less height than 
width show a much greater strength than tests made on cubes of the 
same material, which shows that the bearing strength of rock on 
which foundations are built is much greater than the cubes of 
this stone. In Table I, Part I, the lowest value given for the 
crushing strength of a cube is 2,894 pounds per square inch, which 
is equal to 416,736 pounds per square foot. This shows that any 
ordinary stone which is well imbedded will carry any load of masonry 
placed on it. 

174. Sand and Gravel. Sand and gravel are often found to- 
gether. Gravel alone, when of sufficient thickness, makes one of the 
firmest and best foundations. Dry sand or wet sand, when pre- 
vented from spreading laterally, forms one of the best beds for foun- 
dations; but it must be well protected from running water, as it is 
easily moved by scouring. Clean, dry sand will safely support a load 
of 3,000 to 8,000 pounds per square foot; and when compact and well 
cemented, from 8,000 to 10,000 pounds per square foot. Ordinary 
gravel well bedded will safely bear a load of 6,000 to 8,000 pounds 
per square foot; and when well cemented, from 12,000 to 16,000 
pounds per square foot. 



MASONRY AND REINFORCED CONCRETE 109 

175. Clay. There is great variation in clay soils, ranging from 
a very soft mass which will squeeze out in all directions when a very 
small pressure is applied, to shale or slate which will support a very 
heavy load. As the bearing capacity of ordinary clay is largely 
dependent upon its dryness, it is therefore very important that a 
clay soil should be well drained, and that a foundation laid on such a 
soil should be at a sufficient depth to be unaffected by the weather. 
If the clay cannot be easily drained, means should be taken to prevent 
the penetration of water. When the strata are not horizontal, great 
care must be taken to prevent the flow of the soil under pressure. 
When gravel or coarse sand is mixed with the clay, the bearing capac- 
ity of the soil is greatly increased. 

The bearing capacity of a soft clay is from 2,000 to 4,000 pounds 
per square foot; of a thick bed of medium dry clay, 4,000 to 8,000 
pounds per square foot, and for a thick bed of dry clay, 8,000 to 10,000 
pounds per square foot. 

176. Soft or Semi-Liquid Soils. The soils of this class include 
mud, silt, quicksand, etc., and it is necessary to remove them entirely 
or to reach a more solid stratum under the softer soil; or sometimes 
the soil can be consolidated by adding sand, stone, etc. The manner 
of improving such a soil will be discussed later. In the same way 
that water will bear up a boat, a semi-liquid soil will support, by the 
upward pressure, a heavy structure. For a soil of this kind, it is very 
difficult to give a safe bearing value; perhaps 500 to 1,500 pounds 
per square foot is as much as can be supported without too great a 
settlement. 

177. Improving a Compressible Soil. The general method of 
doing this consists in making the soil more dense. This may be 
done by driving a large number of piles into the soil, especially if the 
piles will be always under the water line in that ground. Driving 
the piles compresses the soil; and if the piles are always under water, 
they will be free from decay. If the soil is sufficiently firm so that 
the pile can be withdrawn and the hole will retain its form even tem- 
porarily, it is better to draw the pile and then immediately fill the 
hole with sand, which is rammed into the hole as compactly as pos- 
sible. This gives us a type of piling known as sand piles. 

A soft, clayey subsoil may frequently be improved by covering it 
with gravel, which is rammed and pressed into the clay. Such a 



110 MASONRY AND REINFORCED CONCRETE 

device is not very effective, but it may sometimes be sufficiently 
effective for its purpose. 

A subsoil is often very soft because it is saturated with water 
which cannot readily escape. Frequently a system of deep drainage 
which will reduce the natural level of the ground-water considerably 
below the desired depth of the bottom of the foundation, will trans- 
form the subsoil into a dry, firm soil which is amply strong for its 
purpose. Even when the subsoil is very soft, it will sustain a heavy 
load, provided that it can be confined. While excavating for the 
foundations of the tower of Trinity Church in New York City, a 
large pocket of quicksand was discovered directly under the proposed 
tower. Owing to the volume of the quicksand, it was found to be 
impracticable to drain it all out; but it was also discovered that the 
quicksand was confined within a pocket of firm soil. A thick layer 
of concrete was then laid across the top, which effectively sealed up 
the pocket of quicksand, and the result has been perfectly sat- 
isfactory. 

178. Preparing the Bed on Rock. The preparation of a rock 
bed on which a foundation is to be placed, is a simple matter com- 
pared with that required for some soils on which foundations are 
placed. The bed-rock is prepared by cutting away the loose and 
decayed portions of the rock and making the plane on which the 
foundation is placed perpendicular to the direction of the pressure. 
If the rock bed is an inclined plane, a series of steps can be made for 
the support of the foundation. Any fissures in the rock should be 
filled with concrete. 

Whenever it is necessary to start the foundation of a structure at 
different levels, great care is required to prevent a break in the joints 
at the stepping places. The precautions to be taken are that the 
mortar-joints must be kept as thin as possible; the lower part of the 
foundations should be laid in cement mortar; and the work should 
proceed slowly. By following these precautions, the settlement in 
the lower part will be reduced to a minimum. These precautions 
apply to foundations of all classes. " 

179. Preparing the Bed on Firm Earth. Under this heading is 
included hard clay, gravel, and clean, dry sand. The bed is prepared 
by digging a trench deep enough so that the bottom of the foundation 
is below the frost line, which is usually 3 to (> feet below the surface. 



MASONRY AND REINFORCED CONCRETE 



111 



Some provision, similar to that shown in Fig. 38, should be made for 
drainage. 

Care should be taken to proportion the load per unit of area so 
that the settlement of the founda- 
tion will be uniform. 

ISO. Preparing the Bed on 
Wet Ground. The chief trouble 
in making an excavation in wet 
ground, is in disposing of • the '//\w/\\v/,\v 
water and preventing the wet soil 




from flowing into the excavation. 
In moderately wet soils, the area 
to be excavated is enclosed with 
sheet piling (see Fig. 39). This 
piling usually consists of ordinary 
plank 2 inches thick and 6 to 10 
inches wide, and is often driven 7/7 






4 



A^'W,','.^ 










- '•-*:>■ 



.'A 



^ •/>/ 



Fig. 38. Drainage of Foundation Wall 

KM 






Cross Braces 
If 2" Plank 



P 



i 



yy 



g 



6-6 



77777777777 



i 



I 



by hand; or it may be driven by 
methods that will be described 
later. The piling is driven in 
close contact, and in very wet 
soil it is necessary to drive a 
double row of the sheeting. To 
prevent the sheeting from being 
forced inwards, cross-braces are 
used between the longitudinal 
timbers. When one length of 
sheeting is not long enough, an 
additional length can be placed 
inside. A more extended discus- 
sion o£- pile-driving will be given 
in the treatment of the subject of 
"Piles." 

The water can sometimes 
be bailed out, but it is generally 
necessary to use a hand or steam pump to free the excavation of 
water. Quicksand and very soft mud are often pumped out along 
with the water by a centrifugal or mud pump. 






W777 

I 



Fig. 39. Sheet Piling in Foundation 
Trenches. 



112 



MASONRY AND REINFORCED CONCRETE 



Sometimes areas are excavated by draining the water into a hole 
the bottom of which is always kept lower than the general level of 
bottom of the excavation. A pump may be used to dispose of the 
water drained into the hole or holes. 

When a very soft soil extends to a depth of several feet, piles are 
usually driven at uniform distances over the area, and a grillage is 
constructed on top of the piles. This method of constructing a 
foundation is discussed in the section on "Piles." 

181. Footings. The three requirements of a footing course are : 

(1) That the area shall be such that the total load divided by the area 
shall not be greater than the allowable unit-pressure on the subsoil. 

(2) That the line of pressure of the wall (or pier) shall be directly over 
the center of gravity (and hence the center of upward pressure) of the base of 

the footings. 

(3) That the footing shall have 
sufficient structural strength so that 
it can distribute the load uniformly 
over the subsoil. 

When it has been deter- 
mined with sufficient accuracy 
how much pressure per square 
foot may be allowed on the sub- 
soil (see sections 172-176), and 
when the total load of the struc- 
ture has been computed, it is a 
very simple matter to compute 
the width of continuous footings 
or the area of column footings. 

The second requirement is very easily fulfilled when it is possible 
to spread the footings in all directions as desired, as shown in Fig. 43. 
A common exception occurs when putting up a building which entirely 
covers the width of the lot. The walls are on the building line; the 
footings can expand inward only. The lines of pressure do not co- 
incide, as shown in Fig. 40. A construction as shown in the figure will 
almost inevitably result in cracks in the building, unless some special 
device is adopted to prevent them. One general method is to introduce 
a tie of sufficient strength from a to b. The other general method 
is to introduce cantilever beams under the basement, which either 
extend clear across the building or else carry the load of interior 




Fig. 40. Construction where Lines of Down- 
ward and Upward Pressure on Foot- 
ings do not Coincide. 



MASONRY AND REINFORCED CONCRETE 



113 



columns so that the center of gravity of the combined loads will 
coincide with the central pressure line of the upward pressure of the 
footings. 

The third requirement practically means that the thickness of 
the footing (6c, Fig. 41) shall be great enough so that the footing can 
resist the transverse stresses caused by the pressure of the subsoil on 
the area between c and d. When the thickness must be made very great 
(such as jh, Fig. 42), on account of the wide offset gh, material may 
be saved by cutting out the rectangle ekml. The thickness m o is 
computed for the offset g o, just as in the first case; while the thick- 
ness k m of the second layer may be computed from the offset k /. 
Where the footings are made of stone or of plain concrete, whose 



JSL 



ttmmttmm 



Fig. 41. Transverse Stresses in Footing 
Determining Its Thickness. 



tED: 



(J . o h 



Fig. 42. Saving of Material in Very Thick 
Footing. 



transverse strength is always low, the offsets are necessarily small; 
but when using timber, reinforced concrete, or steel I-beams, the 
offsets may be very wide in comparison with the depth of the footing. 
182. Calculation of Footings. The method of calculation is to 
consider the offset of the footing as an inverted cantilever which is 
loaded with the calculated upward pressure of the subsoil against the 
footing. If Fig. 41 is turned upside down, the resemblance to the 
ordinary loaded cantilever will be more readily apparent. Consider- 
ing a unit-length (/) of the wall and the amount of the offset o (= d c in 
Fig. 41), and calling P the unit-pressure from the subsoil, we have 
P o I as the pressure on that area, and its lever-arm about the point c 
is } o. Therefore its moment = \ P o 2 I. If t represents the thick- 
ness b c of the footing, the moment of resistance of that section 
= ^Rlt 2 , in which R = the unit-compression (or unit-tension) in the 
section. We therefore have the equation: 

\PoH = \Rlt\ 



114 



MASONRY AND REINFORCED CONCRETE 



By transposition, 



'SP 



o _ I R 



...(2) 

The solution 



The fraction - is the ratio of the offset to its thickness! 
t 

of the above equation, using what are considered to be conservatively 

safe values for R for various grades of stone and concrete, is given 

in Table XII. 

TABLE XII 

Ratio of Offset to Thickness for Footings of Various Kinds of Masonry 



Kind of Masonry 


Modulus of 

Rupture 

( Minimum 

and Maximum 

Values) 


o 
< 

> 
< 


< < 

CO 


Pressure on Bottom of Footing 
(Tons per Square Foot) 




0.5 


1.0 


1.5 


2.0 


2.5 


3.0 


3.5 


Granite 
Limestone 
Sandstone 
Concrete (plain) 

1:2:4 

1:3:6 


1,200-1,365 
450- 900 
135-1,100 

400- 480 
213- 246 


1,280 
675 
525 

440 
230 


130 
70 
55 

75 
40 


2.5 
1.8 
1.-6 

1.9 
1.4 


1.8 
1.3 
1.15 

1.35 
1.0 


1.45 
1.05 
0.95 

1.1 

0.8 


1.25 

0.9 

0.8 

0.95 
0.7 


1.1 

0.8 
0.75 

0.85 
0.6 


1.0 

0.75 
0.65 

0.75 
0.55 


0.95 

0.7 

0.6 

0.7 
0.5 . 



183. Example The load on a wall has been computed as 19,030 
pounds per running foot of the wall, which has a thickness of 18 inches just 
above the footing. What must be the breadth and thickness of granite slabs 
which may be used as a footing on soil which is estimated to bear safely a 
load of 2 .0 tons per square foot? 

Solution. Dividing the computed load (19,000) by the allow- 
able unit-pressure (2.0 tons == 4,000 pounds), we have 4.75 feet as 
the required width of the footing. 

\ (4.75 - 1.5) = 1 625 feet, the breadth of the offset (6). 

From the table we find that for a subsoil loading of 2.0 tons per square 
foot, the offset for granite may be 1.25 times its thickness. There- 



fore 



1 .62* 



30 feet = 15.0 inches, is the required thickness of 



25 
the footing. 

The compulation of the dimensions of such lootings when they 
arc made of reinforced concrete is taken up during the development 
of this specialized form of Masonry in Part III. 

Although brick can be used as a footing course, the maximum 



MASONRY AND REINFORCED CONCRETE 115 



possible offset (no matter how strong the brick may be) can only be 
a small part of the length o_ r the brick — the brick being laid perpen- 
dicular to the wall. One requirement of a footing course is that the 
blocks shall be so large that th -y will equalize possible variations in 
the density and compressibility of the subsoil. This cannot be done 
by bricks or small stones. Their use should therefore be avoided in 
footing courses. 

184. Beam Footings. Steel, and even wood, in the form of 
beams, are used to construct very widj offsets. This is possible on 
account of their greater transverse strength. The general method 
of calculation is identical with that given above, the only difference 
being that beams of definite transverse strength are so spaced that 
one beam can safely resist the moment developed in the footing in 
that length of wall. Wood can be used only when it will be always 
under water. Steel beams should always be surrounded by concrete 
for protection from corrosion. 

If we call the spacing of the beams s, the length of the offset o, 
the unit-pressure from the subsoil P, the moment acting on one beam 
= \ Po 2 s. Calling w the width of the beam, t its thickness or depth, 
and R the maximum permissible fibre stress, the maximum permissible 
moment = %R w t 2 . Placing these quantities equal, we have the 
equation: 

\Po 2 s = IRwt 2 (3) 

Having decided on the size of the beam, the required spacing may be 
determined. 

1 85. Example. An 18-inch brick wall carrying a load of 12,000 pounds 
per running foot, is to be placed on a soft, wet soil where the unit-pressure 
cannot be relied on for more than one-half a ton per square foot. What must 
be the spacing of 10 by 12-inch footing timbers of long-leaf yellow pine? 

Solution. The width of the footing is evidently 12,000 -f- 1,000 
= 12 feet. The offset o equals I (12 - 1.5) = 5.25 feet = 63 inches. 
Since the unit of measurement for computing the transverse strength 
is the inch, the same unit must be employed throughout. Therefore 

P= ' ; R = i,2()() pounds per square inch; w = 10 inches; and 

t = 12 inches. Equation (3) may be rewritten: 

_ R w /-' 

s "3?7 2. 



116 MASONRY AND REINFORCED CONCRETE 



Substituting the above values, we have : 

_ 1,200 X 10 X 144 

*" 3X ^-X 3,969 
144 



20.9 inches. 



This shows that the beams must be spaced 20.9 inches apart, center 
to center, or with a clear space between them but little more than 
their width. Under the above conditions, the plan would probably 
be inadvisable, unless timber were abnormally cheap and no other 
method seemed practicable. 

186. Steel I=Beam Footings. The method of calculation is the 
same as for wooden beams, except that, since the strength of I-beams 
is not readily computable except by reference to tables in the hand- 
books published by the manufacturers, such tables will be utilized. 
The tables always give the safe load which may be carried on an 
I-beam of given dimensions on any one of a series of spans varying 
by single feet. If we call W the total load (or upward pressure) to 
be resisted by a single cantilever beam, this will be one-fourth of the 
load which can safely be carried by a beam of the same size and on a 
span equal to the offset. 

187. Example. Solve the previous example on the basis of using 
steel I-beams. 

The offset is necessarily 5 feet 3 inches; at 1,000 pounds per 
square foot, the pressure to be carried by the beams is 5,250 pounds 
for each foot of length of the wall. By reference to the tables and 
interpolating, an 8-inch I-beam weighing 17.75 pounds per linear 
foot will carry about 28,880 pounds on a 5 foot 3 inch span. One- 
fourth of this (or 7,220 pounds) is the load carried by a cantilever of 
that length. Therefore, 7,220 ^ 5,250 = 1.375 feet =16.5 inches, 
is the required spacing of such beams. When comparing the cost of 
this method with the cost of others, the cost of the masonry concrete 
filling must not be overlooked. 

188. Design of Pier Footings. The above designs for footings 
have been confined solely to the simplest case of the footing required 
for a continuous wall. A column or pier must be supported by a 
footing which is offset from the column in all four directions. It is 
usually made square. The area is very readily obtained by dividing 
the total load by the allowable pressure per square foot on the soil. 
The quotient is the required number of square feet in the area of the 



MASONRY AND REINFORCED CONCRETE 



117 



footing. If a square footing is permissible (and it is usually prefer- 
able), the square root of that number gives the length of one side of 
the footing. Special circumstances frequently require a rectangular 
footing or even one of special shape. The problem of designing a 
footing so that the center of pressure of the load on a column shall be 
vertical over the center of pressure of the subsoil, is usually even 
more complicated 
than the problem 
referred to in sec- 
tion 189. A col- 
umn placed at the 
corner of a build- 
ing which is lo- 
cated at the ex- 
treme corner of 
the property and 
which cannot ex- 
tend over the prop- 
erty line, must 
usually be sup- 
ported by a canti- 
lever (or by two of 
them at right an- 
gles), balanced at 
the other end by 
the load on an- 
other pier or col- 
umn. While the 
general principle 
involved in such 







• 




, i 


4l ^ ^concrete 


i 
« 


1 i = * 

00 

,T. 


i 


1 








I 


: : : 


| 


v 


i 












i 






i 






i 






i 








, L 












i *• 


-3WJ— > 


1 - 


) 

> 




I 


| C 




1 S 
















i 






























i 


1 \ 


■ 


i. 


, .. 




i x 




'1 



Fig. 43. Grillage of I-Beams. 



methods of construction is very simple, a correct solution often 
requires the exercise of considerable ingenuity. 

The determination of the thickness of such a footing depends 
somewhat upon the method used. When the grillage is constructed 
of I-beams as illustrated in Fig. 43, the required strength of each 
series of beams is readily computed from the offset of each layer. 
If the footing consists of a single block of stone or a plate of concrete, 
either plain or reinforced, the thickness must be computed on the 



118 MASONRY AND REINFORCED CONCRETE 

basis of the mechanics of a plate loaded on one side with a 
uniformly distributed load and on the other side with a load which 
is practically concentrated in the center. The theory of the stresses 
in such a plate is very complicated. It is usually considered safe 
to design the footing in each direction on the basis of one-half 
the actual loading. 

189. Example. A column 3 feet 4 inches square, carrying a total load 
of 630,000 pounds, is to be supported on a soil on which the permissible 
loading is estimated as three tons per square foot; an I-beam footing is to be 
used. Required, the design of. the I-beams. 

Solution. The required area of the footing is evidently 630,000 
~ 6,000 == 105 square feet. Using a footing similar to that illus- 
trated in Fig. 43, we shall make the lower layer of the footing, say 
10 feet 6 inches by 10 feet wide. The length of the beams being 126 
inches, and the column being 40 inches square, the offset from the 
column is 43 inches ( = 3 . 58 feet) on each side. Looking at a table 
of standard I-beams, we find that an 8-inch beam weighing 17.75 

' DO 

pounds per linear foot will carry 37,920 pounds on a span of four feet. 

For a span of 3 . 58 feet, the allowable load is |^? X 37,920, or 42,368 

3.58 

pounds. Taking one-fourth of this, as in the example in section 187, 

we have 10,592 pounds which may be carried by each beam acting as 

a cantilever. The upward pressure on an offset 3.58 feet long and 1 

foot wide, at the rate of 6,000 pounds per 'square foot, would be 

21,500 pounds. Therefore, if two 8-inch beams were placed in each 

foot of width, they would carry the pressure. Therefore 20 such 

beams, each 10 feet 6 inches long, would be required in the lower 

layer. The upper layer must consist of beams 10 feet long on which 

the offset from the pier is 40 inches on each side. The group of 

beams under each of these upper offsets carries an upward pressure 

of 6,000 pounds per square foot on an area 10 feet 6 inches by 3 feet 

4 inches; total pressure, 210,000 pounds. The total load on each foot 

of width of the upper layer is 63,000 pounds. Looking at the tables, 

a 12-inch I-beam weighing 40 pounds per foot can carry a load, on a 

10-foot span, of 43,720 pounds. The permissible load on a cantilever 

of this length would be one-fourth of this, or 10,930 pounds. The 

permissible load on a cantilever 3 feet 4 inches long will be in the ratio 

of 10 feet to 3 feet 4 inches, or, in this case, exactly three times as 




REINFORCED-CONCRETE WATER TANK, ANAHEIM, CALIFORNIA 

Total height, 113 ft. : supporting frame, 75 ft, high; tank, 38 ft. high, 32 ft. in diameter, with 
walls o in. thick at bottom, tapering to 3 in. thick at top. Capacity, 200,000 gallons. Cost, 
$11,400, or 1 5 per cent of lowest estimate on a steel tank and tower of like dimensions. 




CONCRETE MIXER USED IN CONSTRUCTION OF TUNNEL UNDER DETROIT RIVER 

Note the large bin above the mixer, for cement and gravel; also the shaft down which 
the concrete is passed through a chute. 



MASONRY AND REINFORCED CONCRETE 119 

much, which would be 32,790 pounds. If, therefore, such beams are 
placed 6 inches apart, their strength would be slightly in excess of 
that required. Or, as a numerical check, the total of 210,000 pounds, 
divided by 32,790, will show that although seven such beams will have 
a somewhat excessive strength, six would be hardly sufficient; there- 
fore seven beams should be used. It should not be forgotten that 
surrounding all these beams in both layers with concrete adds very 
largely to the strength of the whole footing, but that no allowance is 
made for this additional strength in computing dimensions. It 
merely adds an indefinite amount to the factor of safety. 

PILE FOUNDATIONS 

190. Piles. The term pile is generally understood to be a stick 
of timber driven in the ground to support a structure. This stick of 
timber is generally thought of as the body of a small tree; but timber 
in many shapes is used for piling. Sheet piling, for example, is gen- 
erally much wider than thick. Cast iron and wrought iron have also 
been used for all forms of piling. Structural steel has also been 
used for this purpose. Within the last few years, concrete and 
reinforced concrete piles have been used quite extensively in place of 
wood piles. 

191. Cast=Iron Piles. Cast-iron piles have been used to some 
extent. The advantages claimed for these piles are that they are 
not subject to decay; they are more readily driven than wooden piles 
in stiff clays or stony ground ; and they have a greater crushing strength 
than wooden piles. The latter quality will apply only when the pile 
acts as a column. The greatest objection to these piles is that they 
are deficient in transverse strength to resist sudden blows. This 
objection applies only in handling them before they are driven, and 
to those which, after being driven, are exposed to blows from ice and 
logs, etc. When driving cast-iron piles, a block of wood is placed on 
top of the pile to receive the blow; and, after being driven, a cap with 
a socket in its lower side is placed upon the pile to receive the load. 
Generally lugs or flanges are cast on the sides of the piles, to which 
bracing may be attached for fastening them in place. 

192. Steel Sections. Structural steel sections, as well as many 
special sections, are being used for piling. This form of piling is 
generally used for dams, cofferdams, or locks, and seldom or never 



120 



MASONRY AND REINFORCED CONCRETE 



Trieste d 



< 



United States 



used as bearing piles. Fig. 44 illustrates some of these sections of 

piling. 

193. Screw Piles. This term refers to a type of metal pile whose 

use is limited, but which is apparently very effective where it has 

been used. It consists essentially of a steel shaft, 3 to 8 inches in 

diameter, strong enough to 
act as a column, and also to 
withstand the twisting to 
which it is subjected while 
the pile is being sunk (see Fig. 
45). At the lower end of the 
shaft is a helicoidal surface 
having a diameter of perhaps 
five feet. Such piles can be 
used only in comparatively 
soft soil, and their use is prac- 
tically confined to foundations 
in sandbanks on the shore of 
the ocean. To sink such piles, 
they are screwed into place by 
turning the vertical shaft with 
a long lever. Such a sinking 
is usually assisted by a water- 
jet, as will be described later. 
194. Disc Piles. A varia- 
tion of the screw pile is the 




Wemtinqer (Corruqatedj 



j- 



€ 



Qu.im.by 



I 



Ja.ck.son 



Spring Lock 
Fig. 44. Types of Sheet-Steel Piling. 



disc pile (Fig. 46), which, as its name implies, has a circular disc 
in place of a helicoidal surface. Such a pile can be sunk only by 
use of a water-jet, the pile being heavily loaded so that it shall 
be forced down. 

195. Sheet Piles. Ordinary planks, two or more inches thick, 
and wider than they are thick, are, when driven close together, known 
as sheet piling. The leakage between the piles may be very materially 
diminished by using piles which interlock with each other instead 
of making merely a butt joint. (See Fig. 47.) The simplest form is 
the ordinary tongue-and-groove joint similar to that of matched 
boarding. A development of this in timber sheet piling is a combina- 
tion of three planks which are so bolted together as to make a large- 



MASONRY AND REINFORCED CONCRETE 



121 



scale tongue and groove on each side. The increasing cost of timber, 
and the large percentage of deterioration and destruction during its 
use for a single cofferdam, have developed the manufacture of steel 
sheet filing, which can be redrawn and used many times. The forms 




Fig. 45. Screw Pile. 



Fig. 46. Disc Pile. 



of steel for sheet piling are nearly all patented. The cross-sections 
of a few of them are shown in Fig. 44. One feature of some of the 
designs is the possible flexibility secured in the outline of the dam 
without interfering with the water-tightness. 

Sheet piling is usually driven in close contact (as shown in Fig. 
48), either to prevent leakage, or to confine puddle in cofferdams, to 



jO 0- 



4r 



2 Plank 




Fig. 47. Lapped Sheet-Piling. 



Fig. 48. Single and Sheet Piling 
Plan View. 



prevent the materials of a foundation from spreading, or to guard a 
foundation from being undermined by a stream of water. To make 
wooden piles drive with their parts close against each other, they are 
cut obliquely at the bottom, as shown in Fig. 49. They are kept 
in place while being driven, by means of two longitudinal stringers or 



122 



MASONRY AND REINFORCED CONCRETE 



wales. These wales are supported by gauge-piles previously driven, 
which are several feet apart. Sheet piling is seldom used as bearing 
piles. 

196. Wooden Bearing Piles. Specifications for wooden piles 
generally require that they shall have a diameter of from 7 to 10 
inches at the smaller end, and 12 to 15 inches at the larger end. 
Older specifications were quite rigid in insisting that the tree trunks 
should be straight, and that the piles should be free from various 



VWWAM^ 




\AAJ 



*AM 



Fig. 49. Bevel Point for Sheet Pile. 




Fig. 50. Wrought-Iron Pile-Shoe. 



kinds of minor defects; but the growing scarcity of timber is modify- 
ing the rigidity of these specifications, provided the most essential 
qualifications of strength and durability are provided for. Timber 
piles should have the bark removed before being driven, unless the 
piles are to be always under water. They should be cut square at 
the driving end, and pointed at the lower end. When they are to be 
driven in hard,- gravelly soil, it is often specified that they shall be 
shod with some form of iron shoe. This may be done by means of 
two straps of wrought iron, which are bent over the point so as to 



MASONRY AND REINFORCED CONCRETE 



123 




form four bands radiating from the point of the pile (see Fig. 50). 
By means of holes through them, these bands are spiked to the piles. 
Another method, although it is considered less effective on account 
of its liability to be displaced during driving, is to use a cast-iron shoe. 
These shoes are illustrated in Fig. 51. It is sometimes specified 
that piles shall be driven with the butt end 
or larger end down, but there seems to be 
little if any justification for such a speci- 
fication. The resistance to driving is con- 
siderably greater, while their ultimate bear- 
ing power is but little if any greater. If 
the driving of piles is considered from the 
standpoint of compacting the soil (as al- 
ready discussed in section 177), then driv- 
ing the piles with the small end down will 
compact the soil more effectively than driv- 
ing them butt end down. 

White pine, spruce, or even hemlock 
may be used in soft soils; yellow pine in 
firmer ones; and oak, elm, beech, etc., in 

the more compact soils. They are usually driven from 2\ to 4 feet 
apart each way, center to center, depending on the character of the 
soil and the load to be supported. Timber piles, when partly above 
and partly under water, will decay very rapidly at the water line. 
This is owing to the alternation of dryness and wetness. In tidal 
waters, they are destroyed by the marine worm known as the teredo. 

The American Railway Engineering & Maintenance of Way 
Association recommends the following specifications for piling: 

"Piles slut 1 1 be cut from sound, live trees; shall be close-grained and 
solid; free from defects such as injurious ring shakes, large and unsound 
knots, decay, or other defects that will materially impair their strength. 
The taper from butt to top shall be uniform and free from short bends. 

•All piles except foundation piles shall be peeled." 

1 ( .)7. Bearing Power of Piles. Pile foundations act in a variable 
combination of two methods of support. In one case the piles are 
driven into the soil to such a depth that the frictional resistance of 
the soil to further penetration of the pile is greater than any load 
which will be placed on the pile. As the soil becomes more and more 
soft, the frictional resistance furnished by the soil is less and less; 



Fig. 51. Cast-Iron Pile-Shoe. 



124 MASONRY AND REINFORCED CONCRETE 

and it then becomes necessary that the pile shall penetrate to a strata 
of much greater density, into which it will penetrate but little if any. 
Under such conditions, the structure rests on a series of columns 
(the piles) which are supported by the hard subsoil, and whose action 
as columns is very greatly assisted by the density of the very soft soil 
through which the piles have passed. It practically makes but little 
difference which of these methods of support exists in any particular 
case. The piles are driven until the resistance furnished by each pile 
is as high as is desired. The resistance against the sinking of a pile 
depends on such a very large variety of conditions, that attempts to 
develop a formula for that resistance based on a theoretical computa- 
tion taking in all these various factors, are practically useless. There 
are so many elements of the total resistance which are so large, and 
also so very uncertain, that they entirely overshadow the few elements 
which can be precisely calculated. Most formulae for pile-driving 
are based on the general proposition that the resistance of the pile, 
multiplied by its motion during the last blow, equals the weight of the 
hammer multiplied by the distance through which it falls. To express 
this algebraically: 

If R = Resistance of pile; 

s = Penetration of pile during last blow; 

w = Weight of hammer; 

h = Height of fall of hammer; 

then, according to the above principle, we have: 

Rs = wh. 

Practically, such a formula is considerably modified, owing to 
the fact that the resistance of a pile (or its penetration for any blow) 
depends considerably on the time which has elapsed since the previous 
blow. This practically means that it is far easier to drive the pile, 
provided the blows are delivered very rapidly; and also that when a 
pause is made in the driving for a few minutes or for an hour, the 
penetration is very much less (and the apparent resistance very much 
greater), on account of the earth settling around the pile during the 
interval. The most commonly used formula for pile-driving is 
known as the Engineering News formula, which, when used for 
ordinary hammer-driving, is as follows: 

*=iH^ (4) 



MASONRY AND REINFORCED CONCRETE 125 

This formula is fundamentally the same as the formula given above, 
except that, 

R = Safe load, in pounds; 

s = Penetration, in inches, 
%o = Weight of hammer, in pounds; 

h = Height of fall of hammer, in feet. 

In the above equation, s is considered a free-falling hammer 
(not retarded by hammer rope) striking a pile having a sound head. 
If a friction-clutch driver is used, so that the hammer is retarded by 
the rope attached to it, the penetration of the pile is commonly 
assumed to be just one-half what it would have been had no rope 
been attached (that is, had it been free-falling). 

Also, the quantity s is arbitrarily increased by 1, to allow for the 
influence of the settling of the earth during ordinary hammer pile- 
driving, and a factor of safety of 6 for safe load has been used. In 
spite of the extreme simplicity of this formula compared with that 
of others which have attempted to allow for all possible modifying 
causes, this formula has been found to give very good results. When 
computing the bearing power of a pile, the penetration of the pile 
during the last blow is determined by averaging the total penetration 
during the last five blows. 

The pile-driving specifications adopted by the American Rail- 
way Engineering & Maintenance of Way Association, require that, 

"All piles shall be driven to a firm bearing satisfactory to the Engineer, 
or until five blows of a hammer weighing 3,000 pounds, falling 15 feet (or a 
hammer and fall producing the same mechanical effect), are required to 
drive a pile one-half (£) inch per blow, except in soft bottom, when special 
instructions will be given." 

This is equivalent to saying (applying the Engineering News 
formula) that the piles must have a bearing power of 60,000 pounds. 

198. Example 1. The total penetration during the last five blows 
was 14 inches for a pile driven with a 3,000-pound hammer. During these 
blows the average drop of the hammer was 24 feet. How much is the safe 
load? 

2wh 2X3,000X24 . 144,000 oaniA , 

S~TT - axi4) + l = ~37T = 38 ' 919 pounds - 

199. Example 2. It is required (if possible) to drive piles with a 
:;, 000-pound hammer until the indicated resistance is 70,000 pounds. What 
should be the average penetration during the last five blows when the fall is 
25 feet? 



126 MASONRY AND REINFORCED CONCRETE 

7n nno - 2wh 2 X 3,000 X 25 _ 150,000 

' ' S+ 1 ~ S + 1 ~ 8 + 1 

150,000 , _ , . , /..,., 
•-70^00"- - 1 - 2 - 14 " 1 = 1- 14mcl.es. 

200. The last problem suggests a possible impracticability, 
for it may readily happen that when the pile has been driven to its 
full length its indicated resistance is still far less than that desired. 
In some cases, such piles would merely be left as they are, and addi- 
tional piles would be driven beside them, in the endeavor to obtain 
as much total resistance over the whole foundation as is desired. 

The above formula applies only to the drop-hammer method of 
driving piles, in which a weight of 2,500 to 3,000 pounds is raised 
and dropped on the pile. 

When the steam pile-driver is used, the blows are very rapid, 
about 55 to 65 per minute. On account of this rapidity the soil does 
not have time to settle between the successive blows, and the pene- 
tration of the pile is much more rapid, while of course the resistance 
after the driving is finished is just as great as is secured by any other 
method. On this account, the above formula is modified so that the 
arbitrary quantity added to s is changed from one to 0.1, and the 
formula becomes: 

*=TO ( 5 ) 

201. Methods of Driving Piles. There are three general 
methods of driving piles — namely, by using (1) a falling weight; 
(2) the erosive action of a water-jet; or (3) the force of an explosive. 
The third method is not often employed, and will not be further dis- 
cussed. In constructing foundations for small highway bridges, 
well-augers have been used to bore holes, in which piles are set and 
the earth rammed around them. 

202. Drop-Hammer Pile-Driver. This method of driving piles 
consists in raising a hammer made of cast iron, and weighing from 
2,500 to 3,000 pounds, to a height of 10 to 30 feet, and then allowing 
it to fall freely on the head of the pile. The weight is hoisted by 
means of a hoisting engine, or sometimes by horses. When an engine 
is used for the hoisting, the winding drum is sometimes merely 
released, and the weight in falling drags the rope and turns the hoist- 
ing drum as it falls. This reduces the effectiveness of the blow, and 



MASONRY AND REINFORCED CONCRETE 127 

lowers the value of s in the formula given, as already mentioned. 
To guide the hammer in falling, a frame, consisting of two uprights 
called leaders, about 2 feet apart, is erected. The uprights are 
usually wooden beams, and are from 10 to 60 feet long. Such a 
simple method of pile-driving, however, has the disadvantage, not 
only that the blows are infrequent (not more than 20 or even 10 per 
minute), but also that the effectiveness of the blows is reduced on 
account of the settling of the earth around the piles between the 
successive blows. On this account, a form of pile-driver known as 
the si cam file-driver is much more effective and economical, even 
though the initial cost is considerably greater. 

203. Steam-Hammer File-Driver. The steam pile-driver is 
essentially a hammer which is attached directly to a piston in a steam 
cylinder.. The hammer weighs about 4,000 pounds, is raised by 
steam to the full height of the cylinder, which is about 40 inches, and 
is then allowed to fall freely. Although the height of fall is far less 
than that of the ordinary pile-driver, the weight of the hammer is 
about double, and the blows are very rapid (about 50 to 65 per 
minute). As before stated, on account of this rapidity, the soil does 
not have time to settle between blows, and the penetration of the 
pile is much more rapid, while, of course, the ultimate resistance 
after the driving is finished, is just as great as that secured by any 
other method. 

204. Driving Piles with Water-Jet. When piles are driven in a 
situation where a sufficient supply of water is available, their resist- 
ance during driving may be very materially reduced by attaching a 
pipe to the side of the pile and forcing water through the pipe by 
means of a pump. The water returns to the surface along the sides 
of the pile and thus reduces its frictional resistance. The water also 
softens and scours out the soil immediately underneath the pile, 
and enables the pile to penetrate the soil much more easily. In very 
soft soils, piles may be thus driven by merely loading a comparatively 
small weight on top of the pile while the force pump is being operated ; 
and yet the resistance shortly after stopping the pump will be found 
to be very great. Of course the only method of testing such resist- 
ance is by actually loading a considerable weight on the pile. This 
method of using a water-jet is chiefly applicable in structures which 
are on the banks of streams or large bodies of water. The water-jet 



128 MASONRY AND REINFORCED CONCRETE 

and the hammer are advantageously used together, especially in stiff 
clay. 

205. Splicing Piles. On account of the comparatively slight 
resistance offered by piles in swampy places, it sometimes becomes 
necessary to splice two piles together. The splice is often made by 
cutting the ends of the piles perfectly square so as to make a good 
butt joint. A hole 2 inches in diameter and 12 inches deep is bored 
in each of the butting ends, and a dowel-pin 23 inches long is driven 
in the hole bored in the first pile; the second pile is then fitted on the 
first one. The sides of the piles are then flattened, and four 2 by 4- 
inch planks, 4 to 6 feet long, are securely spiked on the flattened sides 
of the piles. Such a joint is weak at its best, and the power of lateral 
resistance of a joint pile is less than would be expected from a single 
stick of equal length. Nevertheless, such an arrangement is in some 
cases the only solution. 

206. Pile Caps. One practical trouble in driving piles, espe- 
cially those made of soft wood, is that the end of the pile will become 
crushed or broomed by the action of the heavy hammer. Unless this 
crushed material is trimmed off the head of the pile, the effect of the 
hammer is largely lost in striking this cushioned head. This crushed 
portion of the top of a pile should always be cut off just before the 
test blows are made to determine the resistance of the pile, since 
the resistance of a pile indicated by blows upon it, if its end is 
broomed, will apparently be far greater than the actual resistance of 
the pile. 

Another advantage of the steam pile-driver is that it does not 
produce such an amount of brooming as is caused by the ordinary 
pile-driver. Whenever the hammer bounces off the head of the pile, 
it shows either that the fall is too great or that the pile has already 
been driven to its limit. Whenever the pile refuses to penetrate 
appreciably for each blow, it is useless to drive it any further, since 
added blows can only have the effect of crushing the pile and render- 
ing it useless. It has. frequently been discovered that piles which 
have been hammered after they have been driven to their limit, have 
become broken and crushed, perhaps several feet underground. 
In such cases, their supporting power is very much reduced. 

Usually about two inches of the head is chamfered off to prevent 
this bruising and splitting in driving the pile. A steel band 2 to 3 



MASONRY AND REINFORCED CONCRETE 



129 



inches wide and J to 1 inch thick, is often hooped over the head of 
the pile to assist in keeping it from splitting. These devices have 
led to the use of a cast-iron cap for the protection of the head of the 
pile. The cap is made with two tapering recesses, one to fit on the 
chamfered head of the pile, and in the other is placed a piece of hard- 
wood on which the hammer falls. The cap preserves the head of 
the pile. 

207. Sawing Off the Piles. When the piles have been driven, 
they are sawed off to bring the top of them to the same elevation so 
that they will have an even bearing surface. When the tops of the 
piles are above water, this sawing is usually done by hand; and when 



.« --v.- .^Concrete \* . v. , v • f • 

TI 



•*fl •"•■• 




<\*fl 






Fig. 52. Concrete Foundation on Wooden 
Piles. 



t ?-Y',\V: , .-f.-.v--.v.:.v:! •./.::%■ 




Fig. 53. Foundation on Wooden Piles. 



under water, by machinery. The usual method of cutting piles off 
under water is by means of a circular saw on a vertical shaft which is 
supported on a special frame, the saw being operated by the engine 
used in driving the piles. 

208. Finishing the Foundations. When the heads of the piles 
are above water, a layer of concrete is usually placed over them, the 
concrete resting on the ground between the piles, as well as on the 
piles themselves. It is necessary to use a thick plate of concrete, so 
that a concentrated load will be distributed over a number of piles 
(see Fig. 52). Sometimes a platform of heavy timbers is constructed 
on top of the piles, to assist in distributing the load; and in this case 
the concrete is placed on the platform (see Fig. 53). 

When the heads of the piles are under water, it is always neces- 
sary to construct a grillage of heavy timber and float it into place, 



130 



MASONRY AND REINFORCED CONCRETE 



unless a cofferdam is constructed and the water pumped out, in 
which case the foundation can be completed as already described. 
The timbers used to cap the piles in constructing a grillage are usually 
about 12 by 12 inches, and are fastened to the head of each pile by a 
drift-bolt (a plain bar of steel). A hole is bored in the cap and into 
the head of the pile, in which the drift-bolt is driven. The section of 
the drift-bolt is always larger than the hole into which it is to be 
driven; that is, if a 1-inch round drift-bolt is to be used, a J-inch 
auger would be used to bore the hole. The transverse timbers of 
the grillage are drift-bolted to the caps. 

209. Concrete and Reinforced-Concrete Piles. A recent devel- 
opment of the use 

Surface |„ ■ >;;■"■„ ■ ■ A ■ &. I 

of concrete and re- 
inforced concrete is 
to construct piles of 
this material. A 
reinforced-concrete 
pile foundation does 
not materially dif- 
fer in construction 
from a timber pile 
foundation. The 
piles are driven and 
capped with con- 
crete ready for the 

Fig. 54. Comparison of Wooden and Concrete Piles. superstructure ill 

the usual manner. In comparing this type of piles with timber 
piles, they have the advantage of being equally durable in a wet 
or dry soil, and the disadvantage of being more expensive in first 
cost. Sometimes their use will effect a saving in the total cost 
of the foundation by obviating the necessity of cutting the piles 
oil' below the water line. The depth of the excavation and the volume 
of masonry may be greatly reduced, as shown in Fig. 54. In this 
figure is shown a comparison of the relative amount of excavation 
which would be necessary, and also of the concrete which would be 
required for the piles, thus indicating the economy which is possible 
in the items of excavation and concrete. There is also shown a 
possible economy in the number of piles required, since concrete piles 




MASONRY AND REINFORCED CONCRETE 131 

can readily be made of any desired diameter, while there is a practical 
limitation of the diameter of wooden piles. Therefore a less number 
of concrete piles will furnish the same resistance as a larger number of 
wooden piles. In Fig. 54 it is assumed that the three concrete piles 
not only take the place of the four wooden piles in the width of the 
foundation, but there will also be a corresponding reduction in the 
number of piles in a direction perpendicular to the section shown. 
The extent of these advantages depends very greatly on the level 
of the ground-water line. When this level is considerably below the 
surface 4 of the ground, the excavation and the amount of concrete 
required in order that the timber grillage and the tops of the piles 
shall always be below the water line will be correspondingly great, 
and the possible economy of concrete piles will also be correspondingly 
great. 

The pile and cap being of the same material, they readily bond 
together and form a monohthic structure. Reinforced-concrete 
piles can be driven in almost any soil that a timber pile can penetrate, 
and they are driven in the same manner as the timber piles. A com- 
bination of the hammer and water-jet has been found to be the most 
successful manner of driving them. The hammer should be heavy 
and drop a short distance with rapid blows, rather than using a light 
hammer dropping a greater distance. For protection while being 
driven, a hollow, cast-iron cap filled with sand is placed on the head 
of the pile. 

Concrete and reinforced-concrete piles may be classified under 
two headings: (a) those where the piles are formed, hardened, and 
driven very much the same as any pile is driven; (b) those where 
a hole is made in the ground, into which concrete is rammed and left 
to harden. 

Reinforced-concrete piles which have been formed on the ground 
are designed as columns with vertical reinforcement connected at 
intervals with horizontal bands. These piles are usually made square 
or triangular in section, and a steel or cast-iron point is used. 

Fig. .V) shows the cross-section of a corrugated pile used in the 
foundations of the buildings for the Simmons Hardware Company, 
Sioux City, Iowa, and for John J. Latteman, Brooklyn, N. Y. The 
pile tapers from 1(> inches at the large end to 11 inches at the 
small end. The reinforcement consists of Clinton electrically-welded 



132 



MASONRY AND REINFORCED CONCRETE 




Fig. 55. Section of Cor- 
rugated Pile. 



fabric, the size being approximately J-inch wires longitudinally, and 
J-inch wires, 12 inches on centers, for the bands. The hole in the 
center is 3| inches at the top, and tapers to 2 inches at the bottom. 
The piles were driven by means of a water- 
jet and hammer. The jet extended through 
the opening in the pile, and protruded three 
inches below the bottom of the pile. The 
pressure of the water was sufficient to dig a 
hole and carry the loosened soil up the corru- 
gations, and the weight of the hammer drove 
the pile down. When the pile was nearly in 
place, the jet was removed, and the hammer 
was used to force the pile until it was solid. 
The cap was made as shown in Fig. 56; and in driving the pile, a 
hammer weighing 2,500 pounds was dropped 25 feet, 20 to 30 times, 
without injury to the head. 

210. Raymond Concrete 
Pile. The Raymond concrete 
pile (Fig. 57) is constructed in 
place. A collapsible steel pile- 
core is encased in a thin, closely- 
fitting, sheet-steel shell. The 
core and shell are driven to the 
required depth by means of a 
pile-driver. The core is so con- 
structed that when the driving 
is finished, it is collapsed and 
withdrawn, leaving the shell in 
the ground, which acts as a 2J<ztRp 
mould for the concrete. When 
the core is withdrawn, the shell 
is filled with concrete, which is 
tamped during the filling proc- 
ess. These piles are usually 
18 inches to 20 inches in diam- 
eter at the top, and 6 inches to 
8 inches at the point. When 
made larger at the small end. 




1 

Hot. 5ection A-B 



56. 



Wooden Buffefx" 
Cushion Head for Driving Piles. 



t is desirable 



the pil< 



can 



be 



The sheet steel used for these 4 piles 



MASONRY AND REINFORCED CONCRETE 



133 



r~ 



is usually No. 20 gauge. When it is desirable to reinforce these piles, 
the bars are inserted in the shell after the core has been withdrawn 
and before the concrete is place'd. 

211. Simplex Concrete Pile. The different methods for pro- 
ducing the Simplex pile cover the two general classifications of 
concrete piles — namely, those 

moulded in place, and those 
moulded above ground and driven 
with a pile-driver. Fig. 5<S shows 
the standard methods of pro- 
ducing the Simplex pile. In Fig. 
58, A shows a cast-iron point 
which has been driven and im- 
bedded in the ground, the con- 
crete deposited, and the form 
partially withdrawn; while B 
shows the alligator point driving 
form. The only difference be- 
tween the two forms shown in 
this figure, is that the alligator 
point is withdrawn and the cast- 
iron point remains in the ground. 
The concrete in either type is 
compacted by its own weight. 
As the form is removed, the con- 
crete comes in contact with the 
soil and is bonded with it. A 
danger in using this type of pile is 

that, if a stream of water is encountered, the cement may be washed 
out of the concrete before it has a chance to set. 

A shell pile and a moulded and driven pile are also produced by 
the same company which manufactures the Simplex, and are recom- 
mended for use under certain conditions. Any of these types of 
piles can be reinforced with steel. This company has driven piles 
20 inches in diameter and 75 feet long. 

212. Steel Piles. In excavating for the foundation of a 16- 
story building at 14th Street and 5th Avenue, New York, a pocket 
of quicksand was discovered with a depth of about 14 feet below the 




Fig. 57. Raymond Concrete Pile. 



134 



MASONRY AND REINFORCED CONCRETE 



bottom of the general excavation. A wall column of the building 
to be constructed was located at this point, with its center only 15 
inches from the party line. The estimated load to be supported by 
this column was about 500 tons. It was finally decided to adopt 
steel piles which would afford the required carrying capacity in a 
small, compact cluster, and would transfer the load as well as the 

other foundations 




■Wire rope fo» pulling form 
•Rope clips 
-Pulling clamps 



Top of concrete filling 




Lndolform jg ;- # 




"TF 1 *" 



Cast Iron Point Driving Form 
Operation Finished Pile 




to the solid rock. 
These piles, 5 in 
number, were driv- 
en very close to an 
existing wall and 
without endanger- 
ing it. Each pile 
was about 15 feet 
long, and was made 
with an outer shell 
consisting of a steel 
pipe | inch thick 
and 12 inches inside 
diameter, filled with 
Portland cement 
concrete, reinforced 
with four vertical 
steel bars 2 inches 
in diameter. This 
gave a total cross- 
sectional area of 
27.2 square inches 
of steel, with an al- 
lowed load of 6,000 pounds per square inch, and 100.5 square inches 
of concrete on which a unit-stress of 500 pounds was allowed. This 
utilizes the bearing strength of the external shell, and enables the 
concrete filling to be loaded to the maximum permitted by the New 
York Building Laws. The tubes and bars have an even bearing on 
hard bed-rock, to which the former were sunk by the use of a special 
air hammer and an inside hydraulic jet. The upper ends of the 
steel tubes and reinforcing bars were cut off after the piles were 



Alliqator Point Driving FoTm 
Operation Finished Pile 



Fig. 58. Standard Simplex Concrete Piles. 



MASONRY AND REINFORCED CONCRETE 135 

driven. The work was done with care, and a direct contact was 
secured between them and the finished lower surfaces of the cast-iron 
caps, without the intervention of steel shims.* 

213. Grillage. A pile supports a load coming on an area of the 
foundation w T hich is approximately proportional to the spacing be- 
tween the piles. This area, of course, is several times the area of the 
top of the pile. It is therefore necessary to cap at least a group of 
the piles with a platform or grillage which not only will support any 
portion of the load located between the piles, but which also will tend 
to prevent a concentration of load on one pile and will distribute the 
load more or less uniformly over all the piles. Sometimes such a 
platform is made of heavy timbers, especially if timber is cheap; but 
this should never be done unless the grillage will be always under 
water; and even under such conditions the increasing cost of timber 
usually makes it preferable to construct the grillage of concrete. A 
concrete grillage is usually laid with its lower surface a foot or two 
below the tops of the piles. The piles are thus firmly anchored 
together at their tops. The thickness of the grillage is roughly pro- 
portional to the load per square foot to be carried. No close calcula- 
tions are possible; a thickness of from 2 to 5 feet is usually made. 
When reinforced-concrete structures are supported on piles or other 
concentrated points of support, the heads of the piles are usually 
connected by reinforced-concrete beams, which will be described in 
Part III. 

214. Cushing Pile Foundation. A combination of steel, con- 
crete, and wooden piles is known as the Cushing pile foundation. A 
cluster of piles is driven so that it may be surrounded by a wrought- 
iron or steel cylinder, which is placed over them, and which is sunk 
into the soil until it is below any chance of scouring action on the 
part of any current of water. The space between the piles and the 
cylinder is then surrounded with concrete. Although the piles are 
subject to decay above the water line, yet they are so thoroughly 
surrounded with concrete that the decay is probably very slow. The 
steel outer casing is likewise subject to deterioration, but the strength 
of the whole combination is but little dependent on the steel. If such 
foundations are sunk at the ends of the two trusses of a bridge, and 



♦Condensed from Engineering Record, February 22, 1908. 



136 MASONRY AND REINFORCED CONCRETE 

are suitably cross-braced, they form a very inexpensive and jet effect- 
ive pier for the end of a truss bridge of moderate span. The end 
of such a bridge can be connected with the shore bank by means of 
light girders, and by this means the cost of a comparatively expensive 
masonry abutment may be avoided. 

215. Cost. In comparing the cost of timber piles and concrete 
or reinforced-concrete piles, the former are found to be much cheaper 
per linear foot than the latter. As already stated, however, there 
are many cases where the economy of the concrete pile as compared 
with the wooden pile is worth considering. In general, the require- 
ments of the work to be done should be carefully noted before the 
type of pile is selected. 

The cost of wooden piles varies, depending on the size and length 
of the piles, and on the section of the country in which the piles can 
be bought. Usually piles can be bought of lumber dealers at 10 to 
20 cents per linear foot for all ordinary lengths; but very long piles 
will cost more. The cost of driving piles is variable, ranging from 
2 or 3 cents to 12 or 15 cents per linear foot. A great many piles 
have been driven for which the contract price ranged from 20 cents 
to 30 cents per linear foot of pile driven. The length of the pile driven 
is the full length of the pile left in the work after cutting off the pile 
at the desired level of the cap. 

The contract price for concrete piles, about 16 inches in 
diameter and 25 to 30 feet long, is approximately SI. 00 per linear 
foot. When a price of SI. 00 per linear foot is given for a pile 
of this size and length, the price will generally be somewhat re- 
duced for a longer pile of the same diameter. Concrete piles have 
been driven for 70 cents per linear foot, and perhaps less; and 
again, they have cost much more than the approximate price of 
SI. 00 per linear foot. 

216. Piles for the Charles River Dam. The first piles driven 
for the Cambridge (Mass.) conduit of the Charles River dam were 
on the Cambridge shore. On January 1, 1907, 9,969 piles had been 
driven in the Boston and Cambridge cofferdams, amounting to 
297,000 linear feet. Under the lock, the average length of the piles, 
after being cut off, was 29 feet; and under the sluices, 31 feet 4 inches. 
The specifications called for piles to be winter-cut from straight, live 
trees, not less than 10 inches in diameter at the butt when cut off in 



MASONRY AND REINFORCED CONCRETE 



137 



the work, and not less than 6 inches in diameter at the small end. 
The safe load assumed for the lock foundations was 12 tons per pile, 
and for the sluices 7 tons per pile. 

The Engineering News formula was used in determining the bear- 
ing power of the piles. The piles under the lock walls were driven 
very close together; and as a result, many of them rose during the 
driving of adjacent piles, and it was necessary to redrive these piles* 

217. Pile Foundation for Sea=Wall at Annapolis. The piles 
for constructing the 
new sea-wall at 
Annapolis, Md., 
ranged in length 
from 70 feet to 110 
feet. On the outer 
end of the break- 
water, piles 70 feet 
to 85 feet were used. 
These piles were in 
one length, single 
sticks. Toward the 
inner end of the 
breakwater, lengths 
of 100 feet to 110 
feet were required. 



Fig. !>9. Section of New Sea-Wall, Annapolis, Maryland. 

Singlesticks of this 

length could not be secured, and it was therefore necessary to re- 
sort to splicing (see Fig. 59). After a trial of several methods, it 
was found that a splice made by means of a 10-inch wrought-iron 
pipe was most satisfactory. When the top of the first pile had been 
driven to within three feet of the water, it was trimmed down to 10 
inches in diameter. On this end was placed a piece of 10-inch 
wrought-iron pipe 10 inches long. The lower end of the top pile 
was trimmed the same as the top of the first pile, and, when raised 
by the leads, was fitted into the pipe and driven until the required 
penetration was reached. The piles were cut off 4} feet below the 
surface of the water, by a circular saw mounted on a vertical shaft. f 




♦See Engineering-Contracting, February 19, 1908. 

tProceedings of the Engineers' Club of Philadelphia, Vol. XXIII, No. 3. 



138 



MASONRY AND REINFORCED CONCRETE 




COFFERDAMS AND CAISSONS 
218. Cofferdams. Foundations are frequently constructed 
through shallow bodies of water by means of cofferdams. - These 
are essentially walls of clay confined between wooden frames, the 
walls being sufficiently impervious to water so that all water and mud 
within the walled space may be pumped out and the soil excavated 

to the desired depth. It is sel- 
dom expected that a cofferdam 
can be constructed which will be 
so impervious to water that no 
pumping will be required to keep 
it clear; but when a cofferdam 
can be kept clear with a moderate 
amount of pumping, the advan- 
tages are so great that its use 
becomes advisable. A dry coffer- 
dam is most easily obtained 
when there is a firm soil, prefer- 
ably of clay, at a moderate depth 
(say 5 feet to 10 feet), into which 
sheet piling may be driven. The 
sheet piles are driven as closely 
together as possible. The bottom 
of each pile (when made of wood) 
is beveled so as to form a wedge 
which tends to force it against 
the pile previously driven (see 
Fig. 49). In this way a fairly 
tight joint between adjacent piles is obtained. Larger piles 
(see Fig. 60, a) made of squared timber are first driven to act 
as guide-piles. These are connected by waling strips (Fig. 60, b), 
which are bolted to the guide-piles and which serve as guides 
for the sheet piling (Fig. 60, c). The space between the two rows 
of sheet piling is filled with puddle, which ordinarily consists chiefly 
of clay. It is found that if the puddling material contains some 
gravel, there is less danger that a serious leak will form and enlarge. 
Numerous cross-braces or tie-rods (Fig. 60, d) must be used to pre- 
vent the walls of sheet piling from spreading when the puddle is 



Q: 



y ^7Jy^JT~: 



puddle 



v 



P 



/>'* 



V 



Fig. 



Plan and Cross-Section of a 
Cofferdam. 



MASONRY AND REINFORCED CONCRETE 139 

being packed between them. The width of the puddle wall is usually 
made to vary between three feet and ten feet, depending upon the 
depth of the water. When the sheet piling obtains a firm footing in 
the subsoil, it is comparatively easy to make the cofferdam water- 
tight; but when the soil is very porous so that the water soaks up from 
under the lower edge of the cofferdam, or when, on the other hand, 
the cofferdam is to be placed on a bare ledge of rock, or when the rock 
has only a thin layer of soil over it, it becomes exceedingly difficult to 
obtain a water-tight joint at the bottom of the dam. Excessive 
leakage is sometimes reduced by a layer of canvas or tarpaulin which 
is placed around the outside of the base of the cofferdam, and which 
is held in place by stones laid on top of it. Brush, straw, and similar 
fibrous materials are used in connection with earth for stopping the 
cracks on the outside of the dam, and are usually effective, provided 
they are not washed away by a swift current. 

Although cofferdams can readily be used at depths of 10 feet, 
and have been used in some cases at considerably greater depth, 
the difficulty of preventing leakage, on account of the great water 
pressure at the greater depths, usually renders some other method 
preferable when the depth is much, if any, greater than 10 feet. 

219. Cribs. A crib is essentially a framework (called a bird- 
cage by the English) which is made of timber, and which is filled with 
stone to weight it down. Such a construction is used only when the 
entire timber work will be perpetually under water. The timber 
framework must, of course, be designed so that it will safely support 
the entire weight of the structure placed upon it. The use of such a 
crib necessarily implies that the subsoil on which the crib is to rest 
is sufficiently dense and firm so that it will withstand the pressure of 
the crib and its load without perceptible yielding. It is also neces- 
sary for the subsoil to be leveled off so that the crib itself shall not 
only be level but shall also be so uniformly supported that it is not 
subjected to transverse stresses which might cripple it. This is 
sometimes done by dredging the site until the subsoil is level and 
sufficiently firm. Some of this dredging may be avoided through 
leveling up low spots by depositing loose stones which will imbed 
themselves in the soil and furnish a fairly firm subsoil. Although 
such methods may be tolerated when the maximum unit-loading is not 
great (as for a breakwater or a wharf), it is seldom that a satisfactory 



140 



MASONRY AND REINFORCED CONCRETE 



foundation can be thus obtained for heavy bridge piers and similar 
structures. 

220. Open Caissons. A caisson is literally a box; and an open 
caisson is virtually a huge box which is built on shore and launched in 
very much the same way as a vessel, and which is sunk on the site of 
the proposed pier. (See Fig. 61.) The box is made somewhat larger 
than the proposed pier, which is started on the bottom of the box. 
The sinking of the box is usually accomplished by the building of 





i. ■ j * t >- r~ . J-. '- j t . * . ? ^ " r: 



Fig. 61. Section of Open Caisson. 

the pier inside of the box, the weight of the pier lowering it until it 
reaches the bed prepared for it on the subsoil. The preparation of 
this bed involves the same difficulties and the same objections as 
those already referred to in the adoption of cribs. The bottom of 
the box is essentially a large platform made of heavy timbers and 
planking. The sides of the caissons have sometimes been made so 
that they are merely tied to the bottom by means of numerous tie- 
rods extending from the top down to the extended platform at the 
bottom, where they are hooked into large iron rings. When the pier 
is complete above the water line so that the caisson is no longer 
needed, the tie-rods may be loosened by unscrewing nuts at the top. 
The rods may then be unhooked, and nearly all the timber in the 
sides of the caisson will be loosened and may be recovered* 



MASONRY AND REINFORCED CONCRETE 



141 



221. Hollow Cribs or 
Caissons. The foundation 
for a pier is sometimes 
made in the form of a box 
with walls several feet in 
thickness, but with a large 
opening or well through the 
center. Such piers may be 
sunk in situations where 
there is a soft soil of con- 
siderable depth through 
which tlie pier must pass 
before it can reach the firm 
subsoil. In such a case, the 
crib or caisson, which is 
usually made of timber, may 
be built on shore and towed 
to the site of the proposed 
pier. The masonry work 
may be immediately started ; 
and as the pier sinks into 
the mud, the "masonry work 
is added so that it is al- 
ways considerably above the 
water line. (See Fig. 62.) 
The deeper the pier sinks, 
the greater will be the re- 
sistance of the subsoil, un- 
til, finally, the weight of the 
uncompleted pier is of it- 
self insufficient to cause it 
to sink further. At this 
stage, or even earlier, dredg- 
ing may be commenced by 
means of a clam-shell or 
orange-peel dredging buck- 
et, through the interior well. 
The removal of the earth 




1 r— r t- 
















Open 
Well 






Open 
Well 










- l - i 


i i 


i : 



FiE- 62. Hollow Crib Material. 



142 MASONRY AND REINFORCED CONCRETE 

from the center of the subsoil on which the pier is resting, will cause 
the mud and soft soil to flow toward the center, where it is within 
reach of the dredge. The pressure of the pier accomplishes this. 
The deeper the pier sinks, the greater is its weight and the greater 
its pressure on the subsoil, although this is somewhat counteracted 
by the constantly increasing friction of the soil around the outside 
of the pier. Finally the pier will reach such a depth, and the subsoil 
will be so firm, that even the pressure of the pier is not sufficient to 
force any more loose soil toward the central well. The interior 
well may then be filled solidly with concrete, and thus the entire 
area of the base of the pier is resting on the subsoil, and the unit- 
pressure is probably reduced to a safe figure for the subsoil at that 
depth. 

This principle was adopted in the Hawkesbury bridge in Aus- 
tralia, which was sunk to a depth of 185 feet below high water — 
a depth which would have been impracticable for the pneumatic 
caisson method described later. In this case, the caissons were 
made of iron, elliptical in shape, and about 48 feet by 20 feet. There 
were three tubes 8 feet in diameter through each caisson. At the 
bottom, these tubes flared out in bell-shaped extensions which formed 
sharp cutting edges with the outside line of the caisson. These bell- 
mouthed extensions thus forced the soil toward the center of the 
wells until the material was within reach of the dredging buckets. 

This method of dredging through an opening is very readily 
applicable to the sinking of a comparatively small iron cylinder. As 
it sinks, new sections of the cylinder can be added; while the dredge, 
working through the cylinder, readily removes the earth until the 
subsoil becomes so firm that the dredge will not readily excavate it. 
Under such conditions the subsoil is firm enough for a foundation, 
and it is th en only necessary to fill the cylinder with concrete to ob- 
tain a solid pier on a good and firm foundation. 

One practical difficulty which applies to all of these methods of 
cribs and caissons, is the fact that the action of a heavy current in a 
river, or the meeting of some large obstruction such as a boulder or 
large sunken log, may deflect the pier somewhat out of its intended 
position. When such a deflection takes place, it is difficult if not 
impossible to force the pier back to its intended position. It there- 
fore becomes necessary to make the pier somewhat larger than the 



MASONRY AND REINFORCED CONCRETE 143 

strict requirements of the superstructure would demand, so that the 
superstructure may have its intended alignment, even though the 
pier is six inches or even a foot out of its intended position. 

222. Pneumatic Caissons. A pneumatic caisson is essentially 
a large inverted box on which a pier is built, and inside of 
which work may be done because the water is forced out of 
the box by compressed air. If an inverted tumbler is forced 
down into a bowl of water, the large air space within the tum- 
bler gives some idea of the possibilities of working within the 
caisson. If the tumbler is forced to the bottom of the bowl, the 
possibilities of working on a river bottom are somewhat exem- 
plified. It is, of course, necessary to have a means of communi- 
cation between this working chamber and the surface; and it is 
likewise necessary to have an air-lock through which workmen (and 
perhaps materials) may pass. 

The process of sinking resembles in many points that described 
in the previous section. The caisson is built on shore, is launched, 
and is towed to its position. Sometimes, for the sake of economy 
(provided timber is cheap), that portion of the pier from the top of 
the working chamber to within a few feet below the low-water line, 
may be built as a timber crib and filled with loose stone or gravel 
merely to weight it down. This method is usually cheaper than 
masonry; and the timber, being always under water, is durable. As 
in the previous section, the caisson sinks as the material is removed 
from the base, the sinking being assisted by the additional weight 
on the top. The only essential difference between the two processes 
consists in the method of removing the material from under the 
caisson. The greatest depth to which such a caisson has ever been 
sunk is about 110 feet below the water line. This depth was reached 
in sinking one of the piers for the St. Louis bridge. At such depths 
the air pressure per square inch is about 48 pounds, which is between 
three and four times the normal atmospheric pressure. Elaborate 
precautions are nece°s?ry to prevent leakage of air at such a pressure. 
Only men with strong constitutions and in perfect health can work 
in such an air pressure, and even then four hours work per day in two 
shifts of two hours each is considered a good day's work at these 
depths. The workmen are liable to a form of paralysis which is 
called caisson disease, and which, especially in those of weak constitu- 



144 



MASONRY AND REINFORCED CONCRETE 



tion or intemperate habits, will result in partial or permanent dis- 
ablement and even death. 

In Fig. 63 is shown an outline, with but few details, of the 
pneumatic caisson used for a large bridge over the Missouri River 
near Blair, Nebraska. The caisson was constructed entirely of 
timber, which was framed in a fashion somewhat similar to that 
shown in greater detail in Fig. 62. The soil was very soft, consisting 




5 and 
pipes 



Air lock 



/Trusses 



Fig. 63. Outline of Pneumatic Caisson. 



chiefly of sand and mud, which was raised to the surface by the 
operation of mud pumps that would force a stream of liquid mud 
and sand through the smaller pipes, which are shown passing through 
the pier. The larger pipes near each side of the pier, were kept 
closed during the process of sinking the caisson, and were opened only 
after the pier had been sunk to the bottom, and the working chamber 
was being filled with concrete, as described below. These extra 
openings facilitated the filling of the working chamber with concrete. 
Near the center of the pier, is an air-lock, with the shafts extend- 
ing down to the working chamber and up to the surface. The 
ends of three trusses, which were made part of the construction of 



MASONRY AND REINFORCED CONCRETE 



145 



the caisson in order to resist any tendency to collapse, are also shown. 

A caisson is necessarily constructed in a very rigid manner, the 
timbers being generally 12 by 12-inch, and laid crosswise in alter- 
nate layers, which are thoroughly interlocked. An irregularity in the 
settling may often be counteracted by increasing the rate of excavation 
under one side or the other of the caisson, so that the caisson will be 
guided in its descent in that direction. 

A great economy in the operation of the compressed-air locks is 
afforded by combining the pneumatic process with the open-well 
process described in the previous 
section, by maintaining a pit in 
the center of the caisson. A 
draft tube which is as low as the 
cutting edge of the caisson pre- 
vents a blow-out of air into the 
central well. The material dug 
by the workmen in the caisson is 
thrown loosely into the central 
well or sump, from which it is 
promptly raised by the dredging 
machinery (see Fig. 64). By the 
adoption of this plan, the air-lock 

needs to be used only for the entrance and exit of the workmen 
to and from the working chamber. 

When the caisson has sunk to a satisfactory subsoil, and the 
bottom has been satisfactorily cleaned and leveled off, the working 
chamber is at once filled with concrete. As soon as sufficient con- 
crete has been placed to seal the chamber effectively against the 
entrance of water, the air-locks may be removed, and then the com- 
pletion of the filling of the chamber and of the central shaft is merely 
open-air work. 

RETAINING WALLS 

223. A retaining wall is a wall built to sustain the pressure of a 
vertical bank of earth. The stability of the wall is a comparatively 
simple matter when three quantities have been determined : 

(1) The intensity of the earth pressure; 

(2) The point of application of the resultant of the earth pressure; 

(3) The line of action of this pressure. 




Fig. 64. Combination of Pneumatic Cais- 
son and Open- Well Methods. 



146 



MASONRY AND REINFORCED CONCRETE 



Unfortunately, earthy material is very variable in its action in these 
respects, depending on its condition. It is not only true that different 
grades of earthy material act quite differently in these respects, but 
it is also true that the same material will act differently under varying 
physical conditions, especially in regard to its saturation with water. 
On these accounts it is impracticable, even by experiment, to deter- 
mine values which are reliable for all conditions. 

It is also comparatively easy to formulate a theory regarding the 
pressure of earthwork which shall be based on certain theoretical 

assumptions. One of these as- 



fsmcharaed 
* earth* 




Fig. 65. Typical Retaining Wall. 



sumptions is that the so-called 
plane of rupture is a plane surface 
— or, in other words, that the line 
a b (Fig. 65) is a straight line. 
There is considerable evidence, 
and even theoretical grounds, for 
considering not only that the line 
a b is a curved line, but that the 
curve is variable, depending on 
the physical conditions. It is 
also assumed that the earthy ma- 
terial acts virtually the same as a liquid with a density considerably 
greater than water; but there is ground for believing that even 
this assumption is not strictly warranted. Theoretically the prob- 
lem is also very much complicated by the question of the earth 
pressure which may be produced by a surcharged wall. A surcharge 
is a bank of earth which is built above the height of the top of the 
retaining wall and sloping back from it. It certainly adds to the 
pressure on the earth immediately back of the wall itself and in- 
creases the pressure on the wall. 

224. Theoretical Formulae. In spite of the unreliability of 
theoretical formulae, for the reasons given above, certain formulas 
which are here quoted without demonstration are sometimes used for 
lack of better formulae as a guide in determining the thickness of a 
wall. For simplicity it is assumed that the rear face of the wall is 
vertical. The variation in the theory by attempting to allow for a 
slope of the rear face, merely complicates the theory; while the effect 
of such a variation from the vertical as is ever adopted is usually so 



MASONRY AND REINFORCED CONCRETE 



147 



small that it is utterly swallowed up by the unavoidable uncertainties 
in the practical application of the theory. In Fig. 66; 

Let E = Total pressure against rear face of wall on a unit-length of wall; 
w = Weight of a unit-volume of the earth; 
h = Height of \jall; 

cf) = The angle of repose with the horizontal — that is, the angle at 
^ which that kind of earth will remain without further sliding. 

Then, when the upper surface of the earth is horizontal, we have the 
equation : 



E = tan 2 (45°--^ ) 



wh 



(6) 



If the upper surface of the earth is surcharged with a bank of earth 
at a natural slope, or if the angle of slope of the surcharge = j>, then 
the equation becomes: 



E = — cos <}> w h* 



(7) 



w/r?& 




Fig. 



36. Pressure on Retaining Wall. 



An inspection of Equation 6 will show that the pressure E is greater 
for small values of <j>. The angle of repose for various materials is 
not only variable 
for different grades 
of material, but is 
variable for the 
same grade of ma- 
terial under various 
conditions of satu- 
ration. A value of 
4> which is frequent- 
ly adopted is 30°. 

This is considerably lower than the usual true value of 4> for dry 
material, and is usually a safe value of <f> for any material (except 
quicksand) either wet or dry. The adoption of this value, there- 
fore, generally means that the result is safe, and that the factor of 
safety is merely made somewhat larger. 

225. Exam-pie. What will be the pressure per foot of length of the 
wall, for a wall 18 feet high, the angle of repose for the earth being assumed 
at 30°? 

Solution. Here h = 18 feet, and $ = 30°. The weight of 
earth (w) is quoted as varying from 70 to 120 pounds per cubic foot 
according to the degree of saturation and density of packing. When 



148 MASONRY AND REINFORCED CONCRETE 



the earth is densely packed, its angle of repose is greater; therefore 
we are safe in assuming a weight of 100 pounds per cubic foot for an 
angle (<f>) of 30°. Substituting these values in Equation 6, we have : 

g = tanM45°-^) 100 ^ 324 

= tan 2 30° X 16,200 
= 5,400 pounds. 

Using this value of <f> = 30° gives us the simple relation that E = 
\ w h 2 , or one-sixth of the unit-weight of the earth times the square 
of the height, for a wall without a surcharge. 

226. Methods of Failure. There are four distinct ways in 
which failure of a retaining w T all may come about: 

(1) A retaining wall may fail by sliding bodily on its foundations 
or on any horizontal joint. This may occur when the wall is rest- 
ing on a soft soil, and especially when the foundation is not sunk 
sufficiently deep into the subsoil so that it is anchored. The failure 
of the wall on a horizontal joint is very improbable when the masonry 
work and its bonding are properly done. Perfectly flat, continuous 
joints should be avoided. 

(2) A retaining wall may fail by crushing the toe of the wall. 
This may occur provided that the resultant of the weight of the wall 
and of the overturning pressure comes so near the toe of the wall, 
and the intensity of that pressure is so great, that the masonry is 
crushed. The method of calculating such pressure will be given later. 

(3) The wall may fail by tipping over. This may occur pro- 
vided that the resultant pressure (described later) passes outside the 
toe of the wall. 

(4) The same effect occurs provided that the subsoil is unable 
to withstand the concentrated pressure on the toe of the wall, and 
yields, while the masonry of the wall may nevertheless remain intact 
and the wall itself be properly proportioned. 

227. Determining the Resultant Pressure. Assume a very 
simple numerical case, as in Fig. G7. The weight of the wall and its 
line of action are very readily determined with accuracy. The base 
of the wall has been made T \ of the height, or 7.2 feet. The batter 
of the outer face is at the rate of 1 in 5, or is 3.6 feet in the total height 
of the wall, leaving 3.6 feet as the thickness at the top. The area of 
the cross-section = J (3.6 + 7.2) 18 = 97.2 square feet. On the 



MASONRY AND REINFORCED CONrKETE 149 



basis that this masonry weighs 140 pounds per cubic foot, a section of 
this wall one foot long will weigh 13,608 pounds. To find the line of 
application of the weight, we must find the center of gravity of the 
trapezoid, and for this purpose we may divide the trapezoid into a 
rectangle and a right-angled triangle. The rectangle has an area of 
64.8 square feet, and its center of gravity is 1 8 feet from the rear face. 
The center of gravity of the triangle (whose area equals \ X 18 X 3.6 
= 32.4 square feet) is at one-third of the base of the triangle from its 
right-hand vertical edge, or at a distance of 4.8 feet from the rear of 
the wall. The center of gravity of the trapezoid is then found numer- 
ically as follows : 

64.8 X 1.8=116.64 

3 M x48 = i 5 L 52 
97.2 A 272.16 

272.16-97.2 = 2.80 feet, 

which is the distance of the center of gravity of the trapezoid from 
the rear face of the wall. The pressure of the earth on the rear wall, 
as stated above, is very uncertain; a value for it has already been 
computed (in the example in section 225) as 5,400 pounds. This 
value is probably excessive, except under the most unfavorable con- 
ditions. The point of application of the resultant of this pressure, 
as well as the direction of that resultant, is also uncertain, and has 
been the subject of much theoretical controversy. If the soil were 
merely a liquid which had no internal friction, there would be no 
uncertainty. In this case, the point of application of the pressure 
would be at one-third the height of the wall from the base, and its 
direction would be perpendicular to the rear face of the wall. This is 
the most unfavorable condition for stability which could be assumed; 
and on this account, calculations are sometimes made on this basis, 
with the knowledge that if the wall is stable under these most unfavor- 
able conditions, it will certainly be stable no matter what the real 
conditions may be. On this basis we have the resultant pressure 
against the rear of the wall as indicated by the arrow in Fig. 67. The 
resultant pressure on the base of the wall is therefore a line the direc- 
tion of which is indicated by the diagonal of a parallelogram whose 
two sides are parallel to the two forces, the sides being proportional 
to those forces. The amount of this pressure equals the square root 
of the sum of the squares of 5,400 and 13,608, or 14,640 pounds. The 



150 



MASONRY AND REINFORCED CONCRETE 



intersection of this line of pressure with the base is evidently at a dis- 
tance from the intersection of the line of vertical pressure, equal to: 

5,400 



6 feet X 



13,608 



2.38 feet. 



That point is therefore 5.18 feet from the rear of the wall, or 2.02 feet 
from the toe. This point represents the center of pressure of the 

pressure on the subsoil. The pres- 
sure is most intense at the toe of 
the wall, and is there assumed to 
be twice as intense as the average 
pressure. It is also assumed that 
the pressure diminishes toward 
the rear, until, at a distance back 
from the center of pressure equal 
to twice the distance from the 
center of pressure to the toe, the 
pressure is zero. This would 
mean that the pressure varies as 
the ordinates of a triangle (as il- 
lustrated in Fig. 68), the triangle 
having a base of 3 X 2.02 = 
6.06 feet. The average pressure 
would equal 14,640 -J- 6.06 = 
2,415 pounds per square foot. 
The maximum pressure at the 
toe would therefore equal twice 
this average pressure, or 4,830 
pounds per square foot, or about 
34 pounds per square inch. This 
unit-pressure is so far within that allowable for stone masonry, that 
there is no danger of the crushing of the masonry at the toe. 

The pressure on the subsoil, which is less than 2\ tons per square 
foot, is less than that usually allowable on a good subsoil. There is 
therefore but little danger that the subsoil will be crushed and that 
the wall will tip over bodily on account of the failure of the subsoil. 
Since the line of pressure is likewise two feet back of the toe of the 
wall, there is no danger that the wall will tip over around its toe. The 
accuracy with which these calculations have been carried out should 




Fig. 67. 



Resultant Pressure 
Wall. 



of Retaining 



MASONRY AND REINFORCED CONCRETE 



151 



not lead to the idea that the pressures will necessarily be exactly as 
stated, since the calculations are based on assumptions which are at 
the best very doubtful, but which, as previously stated, are probably 
excessively safe. 

The form chosen for this wall is also so simple that a purely 
numerical calculation was the easiest and most satisfactory method. 
If the shape of the wall had been more irregular, it would have been 
easier to adopt the graphical method for the determination both of 
the center of gravity of the wall and of the 
resultant pressure on the subsoil. For in- 
stance, if the rear face of the wall had been 
inclined, the line of pressure would have 
been drawn perpendicular to the rear face 
and through a point at one- third the height 
of the wall. The position of the center of 
gravity of the wall would have been deter- 
mined by the purely graphical method of 
determining the center of gravity of a trap- 
ezoid; and then the amount, direction, and 
intersection of the resultant with the base 
of the wall would have been determined by 
purely graphical methods. 

228. Empirical Rules. On account of the unsatisfactory nature 
of theoretical calculations, retaining walls are usually built by the 
application of purely empirical rules. Trautwine recommends that 
for a wall of cut stone or of first-class large ranged rubble in mortar, 
the thickness should be .35 of its vertical height. For a good common 
mortar rubble or brick, the thickness should be .4, and for a dry wall 
.5, of the height. Military engineers who have a very extensive 
experience in constructing retaining walls as a feature of fortification 
work, use a rule giving much less thickness than this, and make it 
depend on the batter of the wall. The thickness at the base in pro- 
portion to the height, is as follows: 

Gen. Fanshawe's Rule for Thickness of Retaining Walls 




Fig. 68. Variation of Inten- 
sity of Pressure on Base. 



Batter 


1 
s 


* 


* 


1 

IT) 


1 
rs 


it 


Vertical 


Base -s- Height 


24% 


25% 


26% 


27% 


28% 


30% 


32% 



152 



MASONRY AND REINFORCED CONCRETE 



The fact that experience has shown that the above proportions 
are usually safe, provided that the subsoil is sufficiently hard, is 
another proof that the assumptions made in the problem worked out 
above are excessively safe, since Fanshawe's rule would have required 
a ratio of base to height of only 24 per cent, while the ratio chosen for 
the problem was 40 per cent. 

229. Failure of Retaining Walls. It is a significant fact that 
a retaining wall may apparently withstand the pressure against it for 

a period of several years, and 
may then slowly and gradually 
fail. This is sometimes due to 
the action of frost on the soil 
behind the wall. The water ac- 
cumulates behind the wall in the 
early winter, and, if it is unable 
to drain away, may freeze, ex- 
pand, and exert a pressure on 
the wall which forces it out. One 
great precautionary feature in 
the construction of retaining 
walls is to place drain-pipes 
through the wall at sufficient in- 
tervals so that water cannot ac- 
cumulate and remain behind the wall. The gradual failure of 
walls may also be due to the undermining and weakening of the sub- 
soil, which makes it unable to resist the concentrated pressure on the 
toe of the wall. Faulty construction and the violation of the ordinary 
rules of good masonry work — the latter being sometimes done with 
the idea that anything is good enough for a retaining wall — are also 
responsible for some failures, since they prevent the body of the wall 
from acting as a unit in resisting a tendency to overturn. 

The tendency to slide outward at the bottom, and even the 
tendency to overturn, may be materially resisted by making the lower 
course with the joints inclined toward the rear. This method of 
construction is all the more logical, since it makes the joints nearly 
perpendicular to the line of pressure. In fact, the line of pressure is 
really a curved line which is more nearly vertical toward the top of the 
wall, and more and more inclined to the horizontal toward the bottom 




Fig. 



Retaining Wall with. Curved 
Cross-Section. 



MASONRY AND REINFORCED CONCRETE 



153 



of the wall. The recognition of this principle has sometimes resulted 
in designing retaining walls on the principle illustrated in Fig. 69, 
which is somewhat similar to a section of an arch set on end. Such 
curved outlines, of course, are more expensive, and are sometimes 
inconvenient, and for that reason are but seldom adopted. 

A detail which is frequently adopted in the design of retaining 
walls, is to use what is virtually a batter to the rear face of the wall, 
but to accomplish this by a series of steps on the rear of the wall. 
This not only per- 
mits the use of 
rectangular blocks 
of stone and the 
employment of ver- 
tical joints, but also 
adds considerably 
to the stability of 
the wall, since the 
vertical pressure of 
the earth on the 
horiz^Tital steps 
adds considerably 
to the resistance to 
overturning. In 
Fig. 70 is shown a design for a retaining wall made to support a 
railway embankment in a location where the natural surface was so 
steep that the embankment would not readily obtain sufficient sup- 
port. Although this use of a retaining wall is somewhat special, the 
general outline of the design not only conforms to the standards on 
that railroad, but represents good practice and is an illustration of 
many of the points referred to above. It should be noted that in this 
case the total width of the base of the wall is nearly one-half the height. 

BRIDGE PIERS AND ABUTMENTS 
230. Placing of Piers. The outline design of a long bridge 
which requires several spans, involves many considerations : 

(1) If the river is navigable, at least one deep and wide channel 
must be left for navigation. The placing of piers, the clear height 
of the spans above high water, and the general plans of all bridges 




Fig. 70. Retaining Wall for Railroad Embankment. 



154 MASONRY AND REINFORCED CONCRETE 

over navigable rivers, are subject to the approval of the United States 
Government. 

(2) A long bridge always requires a solution of the general 
question of few piers and long spans, or more piers and shorter spans. 
No general solution of the"question is possible, since it depends on the 
required clear height of the spans above the water, on the required 
depth below the water for a suitable foundation, and on several other 
conditions (such as swift current, etc.) which would influence the 
relative cost of additional piers or longer spans. Each case must be 
decided according to the particular circumstances of the case. 

(3) Even the general location of the line of the bridge is often 
determined by a careful comparison, not only of several plans for a 
given crossing, but even a comparison of the plans for several locations. 

231 . Usual Sizes and Shapes of Piers. The requirements for the 
bridge seats for the ends of the two spans resting on a pier, are usually 
such that a pier with a top as large as thus required, and with a proper 
batter to the faces, will have all the strength necessary for the external 
forces acting on the pier. For example, the channel pier of one of the 
large railroad bridges crossing the Mississippi River was capped by a 
course of stonework 14 feet wide and 29 feet long, besides two semi- 
circles with a radius of 7 feet. The footing of this pier was 30 feet 
wide by 70 feet long, and the total height from subsoil to top was 
about 170 feet. This pier, of course, was unusually large. For 
trusses of shorter span, the bridge seats are correspondingly smaller. 
The elements which affect stability are so easily computed that it is 
always proper, as a matter of precaution, to test every pier designed 
to fulfil the other usual requirements to see whether it is certainly safe 
against certain possible methods of failure. This is especially true 
when the piers are unusually high. 

The requirements for supporting the truss are, fortunately, just 
such as give the pier the most favorable formation so that it offers 
the least obstruction to the flow of the current in the river. In other 
words, since the normal condition is for a bridge to cross a river at 
right angles, the bridge piers are always comparatively long (in the 
direction of the river) and narrow in a direction perpendicular to the 
flow of the current. The rectangular shape, however, is modified 
by making both the upper and the lower ends pointed. The pointing 
of the upper end serves the double purpose of deflecting the current, 



MASONRY AND REINFORCED CONCRETE 



155 



Water 



and thus offers less resistance to the flow of the water; and it also 
deflects the floating ice and timber, so that there is less danger of the 
formation of a jam during a freshet. The lower end should also be 
pointed in order to reduce the resistance to the flow of the water. 
The ends of the piers are sometimes made semicircular, but a better 
plan is to make them in the form of two arcs of circles which intersect 
at a point. 

232. Possible Methods of Failure. The forces tending to cause 
a bridge pier to fail in a direction perpendicular to the line of the 
bridge, include the action of 
wind on the pier itself, on the 
trusses, and on a train which 
may be crossing the bridge. 
They will also include the max- 
imum possible effect of floating 
ice in the river and of the cur- 
rent due to a freshet. It is not 
at all improbable that all of 
these causes may combine to 
act together simultaneously. 
The least favorable condition 
for resisting such an effect is 
that produced by the weight of 
the bridge, together with that 
of a train of empty cars, and 
the weight of the masonry of 
the pier above any joint whose 
stability is in question. The 
effects of wind, ice, and current will tend to make the masonry 
slide on the horizontal joints. They will also increase the pressure 
on the subsoil on the downstream end of the foundation of a pier. 
They will tend to crush the masonry on the downstream side, and 
will tend to tip the pier over. 

Another possible method of failure of a bridge pier arises from 
forces parallel with the length of the bridge. The stress produced on 
a bridge by the sudden stoppage of a train thereon, combined 
with a wind pressure parallel with the length of the bridge, will tend 




Fig. 71. Bridge Pier. 



to cause the pier to fail in that direction (see Fig. 71). 



Although 



156 



MASONRY AND REINFORCED CONCRETE 



these forces are never so great as the other external forces, yet the 
resisting power of the pier in this direction is so very much less than 
that in the other direction, that the factor of safety against failure 
is probably less, even if there is no actual danger under any reason- 
able values for these external forces. 

233. Abutment Piers. A pier is usually built comparatively 
thin in the direction of the line of the bridge, because the forces tend- 
ing to produce overturning in that direction are usually very small. 
When a series of stone arches are placed on piers, the thrusts of the 

two arches on each side of a pier 
nearly balance each other, and it 
is only necessary for the pier to 
be sufficiently rigid to withstand 
the effect of an eccentric loading 
on the arches; but if, by any ac- 
cident or failure, one arch is de- 
stroyed, the thrust on such a 
pier is unbalanced and the pier 
will probably be overturned by 
the unbalanced thrust of the ad- 
j oining arch. The failure of tha t 
arch would similarly cause the 
failure of the succeeding pier and arch. On this account a very 
long series of arches usually includes an abutment pier for every 
fourth or fifth pier. An abutment pier is one which has sufficient 
thickness to withstand the thrust of an arch, even though it is not 
balanced by the thrust of an arch on the other side of the pier. 
Abutment piers are chiefly for arch bridges; but all piers should 
have sufficient rigidity in the direction of the line of the bridge 
so that any possible thrust which may come from the action of a truss 
of the bridge may be resisted, even if there is no counterbalancing 
thrust from an adjoining truss. 

234. Abutments. The term abutment usually implies not only 
a support for the bridge, but also what is virtually a retaining wall 
for the bank behind it. In the case of an arch bridge, the thrust of 
the arch is invariably so great that their is never any chance that the 
pressure of the earth behind the abutment will throw the abutment 
over, and therefore the abutment never needs to be designed as a 




Fig. 72. 



Typical Abutment with Flaring 
Wing Walls. 



MASONRY AND REINFORCED CONCRETE 



157 




retaining wall in this case; but when the abutment supports a truss 
bridge which does not transmit any horizontal thrust through the 
bridge, the abutment must be designed as a retaining wall. The 
conditions of stability for such structures have already been discussed. 
This principle of the retaining wall is especially applicable if the 
abutment consists of a perfectly straight wall. There are other forms 
of abutments which tend to prevent failure as a retaining wall, on 
account of their design. 

235. Abutments with Flaring Wing Walls. These are con- 
structed substantially as shown 

in Fig. 72. The wing walls make 

an angle of about 30° to 45° 

with the face of the abutment, 

and the height decreases at such 

a rate that it will just catch the 

embankment formed behind it, 

the slopes of the embankment 

probably being at the rate of 

1.5:1. If the bonding of the 

wing walls, and especially the 

bonding at the junction of the 

wing walls with the face of the 

abutment, are properly done, the 

wing walls will act virtually as 

counterforts and will materially 

assist in resisting the overturning tendency of the earth. The 

assistance given by these wing walls will be much greater as the 

angle between the wing walls and the face becomes larger. 

236. U-Shaped Abutments. These consist of a head wall and 
two walls which run back perpendicular to the head wall (see Fig. 73). 
This form of wall is occasionally used, but the occasions are rare 
when such a shape is necessary or desirable. 

237. T-Shaped Abutments. As the name implies, these consist 
of a head wall which has a core wall extending perpendicularly back 
from the center. The core wall serves to tie the head wall and prevent 
its overturning. Of course such an effect can be produced only by 
the adoption of great care in the construction of the wall, so that the 
bonding is very perfect and so that the wall has very considerable 



Fig. 73. U-Shaped Abutment. 



158 MASONRY AND REINFORCED CONCRETE 

tensile strength; otherwise the core wall could not resist the overturn- 
ing tendency of the earth pressure against the rear faceof the abutment. 

CULVERTS 

238. The term culvert is usually applied to a small waterway 
which passes under an embankment of a railroad or a highway. The 
term is confined to waterways which are so small that standard plans 
are prepared which depend only on the assumed area of waterway 
that is required. Although the term is sometimes applied to arches 
having a span of 10 or 15 feet, or even more, the fact that the struc- 
tures are built according to standard plans justifies the use of the 
term culvert as distinguished from a structure crossing some perennial 
stream where a special design for the location is made. The term 
culvert therefore includes the drainage openings which may be needed 
to drain the hollow on one side of an embankment, even though the 
culvert is normally dry. 

239. Various Types of Culverts. Culverts are variously made 
of cast iron, wrought iron, and tile pipe, wood, stone blocks with large 
cover-plates of stone slabs, stone arches, and plain and reinforced 
concrete; still another variety is made by building two side walls of 
stone and making a cover-plate of old rails. 

240. Culverts made of wood should be considered as temporary, 
on account of the inevitable decay of the wood in the course of a few 
years. When wood is used, the area of the opening should be made 
much larger than that actually required, so that a more permanent 
culvert of sufficient size may be constructed inside of the wooden 
culvert before it has decayed. For present purposes, the discussion 
of the subject of Culverts will be limited to those built of stone and 
concrete. 

241. Stone Box Culverts. The choice of stone as a material for 
culverts should depend on the possibility of obtaining a good quality 
of building stone in the immediate neighborhood. Frequently 
temporary trestles are used when good stone is unobtainable, with 
the idea that after the railroad is completed, it will be possible to 
transport a suitable quality of building stone from a distance and 
build the culvert under the trestle. The engineer should avoid the 
mistake of using a poor quality of building stone for the construction 
of even a culvert, simply because such a stone is readily obtainable. 



MASONRY AND REINFORCED CONCRETE 159 

Since a culvert always implies a stream of water which will have a 
scouring action during floods, it is essential that the side walls of 
culverts should have an ample foundation, which is sunk to such a 
depth that there is no danger that it will be undermined. There are 
cases where a bed of quicksand has been encountered, and where the 
cost of excavating to a firmer soil would be very large. In such a 
case, it is generally possible to obtain a sufficient foundation by con- 
structing a platform or grillage of timber which underlies the entire 
culvert, beneath the floor of the culvert. Of course, timber should 
not be used for the foundation, except in cases where it will always be 
underneath the level of the ground-water and will therefore always 
be wet. If the soil has a character such that it will be easily scoured, 
the floor of the culvert between the side walls should be paved with 
large pebbles, so as to protect it from scouring action. At both ends 
of the culvert, there should always be built a vertical wall which should 
run from the floor of the culvert down to a depth that will certainly 
be below any possible scouring influence, in order that -the side walls 
and the flooring of the culvert cannot possibly be undermined. 

The above specifications apply to all forms of stone culverts, and 
even to arch culverts, except that in the case of the larger arch cul- 
verts the precautions in these respects should be correspondingly 
observed. When stone culverts are built with vertical side walls 
which are from 2 to 4 feet apart, they are sometimes capped with large 
flagstones covering the span between the walls. - The thickness of 
the cover-stone is sometimes determined by an assumption as to the 
transverse strength of the stone, and by applying the ordinary theory 
of flexure. The application of this theory depends on the assumption 
that the neutral axis for a rectangular section is at the center of depth 
of the stone, and that the modulus of elasticity for tension and com- 
pression is the same. Although these assumptions are practically 
true for steel and even wood, they are far from being true for stone. 
It is therefore improper to apply the theory of flexure to stone slabs, 
except on the basis of moduli of rupture which have been experi- 
mentally determined from specimens having substantially the same 
thickness as the thickness proposed. Also, on account of the varia- 
bility of the actual strength of stones though nominally of the same 
quality, a very large factor of safety over the supposed ultimate 
strength of the stone should be used. 



160 MASONRY AND REINFORCED CONCRETE 



The maximum moment at the center of a slab one foot wide 
equals J- Wl, in which W equals the total load on the width of one foot 
of the slab, and I equals the span of the slab, in feet; but by the prin- 
ciples of Mechanics, this moment equals I Rh 2 ,m which R equals the 
modulus of transverse strength, in pounds per square foot; and h equals 
the thickness of the stone, in feet. Placing these two expressions 
equal to each other, and solving for h, we find : 



(8) 



6 
8 


Wl 

R 


/- 


3 Wl 
Til 



242. Example. Assume that a culvert is covered with 6 feet 
of earth weighing 100 pounds per cubic foot. Assume a live load on 
top of the embankment equivalent to 500 pounds per square foot, 
in addition; or that the total load on the top of the slab is equivalent 
to 1,100 pounds per square foot of slab. Assume that the slab is to 
have a span (I) of 4 feet. Then the total load IF on a section of the 
slab one foot wide, will be 1,100 X 4 = 4,400 pounds. Assume that 
the stone is sandstone, with an average ultimate modulus of 525 
pounds per square inch (see Table XII), and that the safe value R is 
assumed to be 55 pounds per square inch, or 144 X 55 pounds per 
square foot. Substituting these values in the above equation for h, 
we find that h equals 1.29 feet, or 15.5 inches. 

The above problem has been worked out on the basis of the live 
load which would be found on a railroad. For highways, this could 
be correspondingly decreased. It should be noted that in the above 
formula the thickness of the stone h varies as the square root of the 
span; therefore, for a span of 3 feet (other things being the same as 

above), the thickness of the stone h equals 15.5 X -\| — = 13.4 inches. 

4 IT 

For a span of 2 feet, the thickness should be 15.5 X \l — = 
11.0 inches. 

Owing to the uncertainty of the true transverse strength of 
building stone, as has already been discussed in the design of Offsets 
for Footings (see sections 181-183), no precise calculation is possible; 
and therefore many box culverts are made according to empirical 
rules, which dictate that the thickness shall be as follows: 



MASONRY AND REINFORCED CONCRETE 



161 



For a 2-foot span, 10 inches; 
For a 3-foot span, 13 inches; 
For a 4-foot span, 15 inches. 

These values are slightly less than those computed above. 

Although a good quality of granite, and especially of bluestone 
flagging, will stand higher transverse stresses than those given above 
for sandstone, the rough rules just quoted are more often used, and 
are, of course, safer. When it is desired to test the safety of stone 
already cut into slabs of a given thickness, their strength may be 



m 






-20-6 


— 1 




■n 1 


h- s 


1 1* 




1 
1 
1 


-Sunk 

WQU 


f 


• — 3'0"- 

ZffrS 


i; 

5 1 1 

i ♦ i 


«. 








n __._ m 




f— j'cT-4*3'-o 


'-*j 


j Cover 1 
, stones' 
1 1 










1 1 


1 
1 . 1 





Plan of head walb 

Fig. 74. Double Box Culvert. 



computed from Equation 8, using the values for transverse stresses 
as already given in Table XII. 

243. Double Box Culverts. A box culvert with a stone top is 
generally limited by practice to a span of 4 feet, although it would, 
of course, be possible to obtain thicker stones which would safely 
carry the load over a considerably greater span. Therefore, when 
the required culvert area demands a greater width of opening than 4 
feet, and when this type of culvert is to be used, the culvert may be 
made as illustrated in Fig. 74, by constructing an intermediate wall 
which supports the ends of the two sets of cover-stones forming the 
top. A section and elevation of a double box culvert of 3 feet span 
and a net height of 3 feet, is shown in Fig. 74. This figure also gives 
details of the wing walls and end walls. The double box culvert 
illustrated in Fig. 75 has two spans, each of 4 feet. The stone used 



162 MASONRY AND REINFORCED CONCRETE 

was a good quality of limestone. The cover-stones were made 15 
inches thick. 

244. End Walls. The ends of a culvert are usually expanded 
into end walls for the retention of the embankment. For the larger 
culverts, this may develop into two wing walls which act as retaining 
walls to prevent the embankment from falling over into the bed of the 
stream. An end wall is especially necessary on the upstream end of 
the culvert, so as to avoid the danger that the stream will scour the 





\ i 






'■■'V.'. :" •I©? ■ ■ • ,- ,' -' 


.•■■ ■■ .■--.' ■■■'.■.■-...'■.■..'■••■■ :"-l - '(*:- 


^J:i4^J 




SHK~-~- ~~, a«M»L 


; " " s '! 


K^0 




■fit J9B 

HUH • ■' m 


ram 

H 

rap 




':'■-■ « ' • '■ • ■ 






- 





Fig. 75. Double Box Culvert, 4 by 3-Foot. 

bank and work its way behind the culvert walls. The end wall is 
also carried up above the height of the top of the culvert, so as to 
guard still further against the washing of earth from the embank- 
ment over the end of the culvert into the stream below. All of these 
details are illustrated in the figures shown. 

Box culverts are sometimes constructed as dry masonry — that is, 
without the use of mortar. This should never be done, except for 
very small culverts and when the stones are so large and regular that 
they form close, solid walls with comparatively small joints. A dry 
wall made up of irregular stones cannot withstand the thrusts which 
are usually exerted by the subsequent expansion of the earth embank- 
ment above it. 



MASONRY AND REINFORCED CONCRETE 163 

245. Plain Concrete Culverts. Culverts may be made of plain 
concrete, either in the box form or of an arched type, and having very 
much the same general dimensions as those already given for stone 
box culverts. They have a great advantage over stone culverts in 
that they are essentially monoliths. If the side walls and top are 
formed in one single operation, the joint between the side walls and 
top becomes a source of additional strength, and the culverts are 
therefore much better than similar culverts made of stone. The 
formula developed above (Equation 8) for the thickness of the con- 
crete slab on top of a box culvert, may be used, together with the 
modulus of transverse strength as given for concrete in Table XII. 
This formula will apply, even though the slab for the cover of the 
culvert is laid after the side walls are built, and the slab is considered 
as merely resting on the side walls. If the side walls and top are 
constructed in one operation so that the whole structure is actually 
a monolith, it may be considered that there is that much additional 
strength in the structure; but it would hardly be wise to reduce the 
thickness of the concrete slab by depending upon the continuity be- 
tween the top and the sides. 

246. Arch Culverts. Stone arches are frequently used for 
culverts in cases where the span is not great, and in which the design 
of the culvert (except for some small details regarding the wing walls) 
depends only on the span of the culvert. The design of some arch 
culverts used on the Atchison, Topeka & Santa Fe Railroad (see Fig. 
76, and also Fig. 74) is copied from a paper presented to the Amer- 
ican Society of Civil Engineers by A. G. Allan, Asso. Mem. Am. Soc. 
C. E. The span of these arches is 14 feet, and the thickness at the 
crown is 18 inches. A photograph of one of these arch culverts, 
which shows also many other details, is reproduced in Fig. 77. 

CONCRETE WALKS 

247. Drainage of Foundations. The excavation should be 
made to a sufficient depth so as to get below the frost line. The 
ground should be tamped thoroughly, and the excavation filled with 
cinders, broken stone, gravel, or brickbat, to within four inches (or 
whatever thickness of slab is to be used) of the top of the grade. The 
foundation should be thoroughly rammed, and by using gravel or 
cinders to make the foundation, a very firm surface can be secured 



164 



MASONRY AND REINFORCED CONCRETE 





Side drains should be put in 
at convenient intervals where 
outlets can be secured. The 
foundation is sometimes 
omitted, even in cold cli- 
mates, if the soil is porous. 
Walks laid on the natural 
soils have proven in many 
cases to be very satisfactory. 
At the Convention of the 
National Cement Users' As- 
sociation, held at Buffalo, 
N. Y., January 21 to 23, 
1908, the Committee on Side- 
walks, Streets, and Floors 
presented the following speci- 
fications for sidewalk founda- 
tions : 

"The ground base shall be 
made as solid and permanent as 
possible. Where excavations or 
fills are made, all wood or other 
materials which will decompose 
shall be removed, and replaced 
with earth or other filling like 
the rest of the foundation. Fills 
of clay or other material which 
will settle after [heavy rains or 
deep frost, should be tamped, 
and laid in layers not more than 
six inches in thickness, so as to 
insure a solid embankment which 
will remain firm after the walk 
is laid. Embankments should 
not be less than 2h feet wider 
than the walk which is to be 
laid. When porous materials, 
such as coal ashes, granulated 
slag, or gravel, are used, under- 
drains of tile should be laid to 
the curb drains or gutters, so as 
to prevent water accumulating 
and freezing under the walk 
and breaking the block." 



MASONRY AND REINFORCED CONCRETE 



165 



248. Concrete Base. The concrete for the base of walks is 
usually composed of 1 part Portland cement, 3 parts sand, and 5 
parts stone or gravel. Sometimes, however, a richer mixture is used, 
consisting of 1 part cement, 2 parts sand, and 4 parts broken stone; 




Fig. 77. Double Arch Culvert, 14 by 5^-Foot. 

but this mixture seems to be richer than what is generally required. 
The concrete should be thoroughly mixed and rammed, and cut into 
uniform blocks. See Fig. 78. The size of the broken stone or 
gravel should not be larger than one inch, vary- 
ing in size down to J inch, and free from fine 
screenings or soft stone. All stone or gravel 
under -J inch is considered sand. 

The thickness of the concrete base will de- 
pend upon the location, the amount of travel, 
or the danger of being broken by frost. The 
usual thickness in residence districts is 3 inches, 
with a wearing thickness of 1 inch, making a 
total of 4 inches. In business sections, the 
walks vary from four to six inches in total thickness, in which 
the finishing coat should not be less then \\ inches thick, 
concrete base is cut into uniform blocks. 




Fig. 78. Square Tamper 



The 



166 



MASONRY AND REINFORCED CONCRETE 



The lines and grades given for walks by the Engineer, should be 
carefully followed. The mould strips should be firmly blocked and 
kept perfectly straight to the height of the grade given. The walks 
usually are laid with a slope of \ inch to the foot toward the curb. 




Fig. 79. Concrete Sidewalk and Curb. 

The blocks are usually from four to six feet square, but some- 
times they are made much larger than these dimensions. The joints 
made by cutting the concrete should be filled with dry sand, and the 
exact location of these joints should be marked on the forms. The 
cleaver or spud that is used in making the joints should not be less 

than \ of an inch or over J of an 
inch in thickness. 

249. Top Surface. The wear- 
ing surface usually consists of 1 
part Portland cement and 2 parts 
crushed stone or good, coarse 
sand, all of which will pass 
through a }-inch mesh screen — 
thoroughly mixed so as to secure 
a uniform color. This mixture 
is then spread over the concrete 
base to a thickness of one inch, 
this being done before the con- 
crete of the base has set or be- 
come covered with dust. The mortar is leveled off with a straight 
edge, and smoothed down with a float or trowel after the sur- 
face water has been absorbed. The exact time at which the 
surface should be floated depends upon the setting of the cement, 





Fig. 



Jointers. 



MASONRY AND REINFORCED CONCRETE 



167 



and must be determined by the workmen; but the final floating 
is not usually performed until the mortar has been in place 
from two to five hours and is partially set. This final floating 
is done first with awooden float, and afterwards with a metal float or 
trowel. The top surface is then cut directly over the cuts made in the 
base, care being taken to cut entirely through the top and base all 
around each block. The joint is then finished with a jointer, Fig. 
80, and all edges rounded or beveled. Care should be taken in the 
final floating or finishing, not to overdo it, as too much working will 
draw the cement to the surface, leaving a thin layer of neat cement, 




Fig. 81. Brass Dot Roller. 



Fig. 82. Brass Line Roller. 



which is likely to peel off. Just before the floating, a very thin layer 
of dryer consisting of dry cement and sand mixed in the proportion 
of one to one, or even richer, is frequently spread over the surface; 
but this is generally undesirable, as it tends to make a glossy walk. A 
dot roller or line roller, Figs. 81 and 82, may be employed to relieve the 
smoothness. 

At the meeting of the National Cement Users' Association 
already referred to, the Committee on Sidewalks, Floors, and Streets 
recommended the following specifications for the top coat: 

"Three parts high-grade Portland cement and five parts clean, sharp 
sand, mixed dry and screened through a No. 4 sieve. In the top coat, the 
amount of water used should be just enough so that the surface of the walk 



168 MASONRY AND REINFORCED CONCRETE 



can be tamped, struck off, floated, and finished within 20 minutes after it is 
spread on the bottom coat; and when finished, it should be solid and not 
quaky." 

In the January, 1907, number of Cement, Mr. Albert Moyer, 
Assoc. M. Am. Soc. C. E., discussing the subject of cement sidewalk 
pavements, gives specifications for monolithic slab for paving pur- 
poses. For an example of this construction, he gives the pavement 
around the As tor Hotel, New York: 

"As an alternative, and instead of using a top coat, make one slab of 
selected aggregates for base and wearing surface, filling in between the frames 
concrete flush with established grade. Concrete to be of selected aggregates, 
all of which will pass through a f-inch mesh sieve; hard, tough stones or 
pebbles, graded in size; proportions to be 1 part cement, 2\ parts crushed 
hard stone screenings or coarse sand, all passing a f-inch mesh, and all 
collected on a i-inch mesh. Tamped to an even surface, prove surface with 
straight edge, smooth down with float or trowel, and in addition a natural 
finish can be obtained by scrubbing with a wire brush and water while con- 
crete is 'green,' but after final set." 

250. Seasoning. The wearing surface must be protected from 
the rays of the sun by a covering which is raised a few inches above 
the pavement so as not to come in contact with the surfaces. After 
the pavement has set hard, sprinkle freely two or three times a day 
for a week or more. 

251. Cost. The cost of concrete sidewalks is variable. The 
construction at each location usually requires only a few days work; 
and the time and expense of transporting the men, tools, and ma- 
terials make an important item. One of the skilled workmen should 
be in charge of the men, so that the expense of a foreman will not be 
necessary. The amount of walk laid per day is limited by the amount 
of surface that can be floated and troweled in a day. If the surfacers 
do not work overtime, it will be necessary to stop concreting in the 
middle of the afternoon, so that the last concrete placed will be in con- 
dition to finish during the regular working hours. The work of con- 
creting may be continued considerably later in the afternoon if a dryer 
concrete is used in mixing the top coat, and only enough water is used 
so that the surface can be floated and finished soon after being placed. 
The men who have been mixing, placing, and ramming concrete 
can complete their day's work by preparing and ramming the founda- 
tions for the next day's work. 

The contract price for a well-constructed sidewalk 4 to 5 inches 



MASONRY AM) REINFORCED CONCRETE 



160 



in thickness, with a granolithic finish, will vary from 15 cents to 30 
cents per square foot. 



CONCRETE CURB 

252. The curb is usually built just in advance of the sidewalk. 
The foundation is prepared similarly to that of walks. The curb is 
divided into lengths similar to that of the walk; and the joints be- 
tween the blocks, and also between the walk and the curb, are made 
similar to the joints between the blocks of the walk. The concrete 
is generally composed of 1 part Portland cement, 3 parts sand, 
and ") parts stone, 



although a richer 



6 -J 



K ■ 

A' .« * 

v. n 



C\2 



tf.Y.'.V 



12' 



© 



1 



f = 



v , \< • v 



*o. v 



• . 

p\ 0. 



v . c\> 



18" 



1 



Fig. 83. Typical Curb Sections. 



mixture is some- 
times used. A 
facing, on the part 
exposed to wear, 
.)f mortar or gran- 
olithic finish, will 
improve the wear- 
ing qualities of the 
curb. 

253. Types 

of Curbing. There are two general types of curb used — a curb 
rectangular in section, and a combined curb and gutter; both 
types are shown in Fig. 83. The foundation for either type is 
constructed in the same manner. Both these types of curb are made 
in place or moulded and set in place like stone curb, but the former 
method is preferable. A metal corner is sometimes laid in the exposed 
vd^v of the curb to protect it from wear. 

254. Construction. The construction of the rectangular section 
is a simple process, but requires care to secure a good job. This is 
usually about 6 inches wide and from 20 to 30 inches deep. After the 
foundation has been properly prepared, the forms are set in place. 
Fig. 84 shows the section of a curb 6 inches wide and 24 inches deep, 
and the forms as they are often used. The forms for the front and 
back each consist of three planks 1J inches thick and 8 inches wide, 
and are surfaced on the side next the concrete. They are held in 
place at ths bottom by the two 2 by 4-inch stakes, and at the top the 



170 



MASONRY AND REINFORCED CONCRETE 



Clamps 









/I- p. 7 .', 



I 



V 



I 



• V .9 

I"x8"-> 



^ 



qKSI 



1 



v 




Fig. 85. Curb Edger. 



Fig. 84. 



Forms for Constructing 
Curb. 



stakes are kept from spreading by a 
clamp. A sheet-iron plate \ inch thick 
is inserted every 6 feet, or at whatever 
distance the joints are made. After the 
concrete has been placed and rammed, 
and has set hard enough to support itself, 
the plate and front forms are removed, 
and the surface and top are finished 
smooth with a trowel; the corner being 

rounded with an edger, as shown in Fig. 85. The joint is usually 

plastered over, and acts as an expansion joint. The forms on 

the back are not removed until the concrete is well set. If a mortar 

or granolithic fin- 
ish is used, a piece 

of sheet iron is 

placed in the form 

one inch from the 

facing, and mortar 

is placed between 

the sheet iron and 

the front form, 

and the coarser 

concrete is placed 

back of the sheet 

iron (Fig. 86). The 

sheet iron is then 

withdrawn and the two concretes thoroughly tamped. 

Fig. 80 shows the section of a combined curb and gutter, and 

the forms that are necessary for its construction. This combination 




Fig. 



Forms for Curb and Gutter. 



MASONRY AND REINFORCED CONCRETE 171 

is often laid on a porous soil without any special foundation, with fair 
results. A 1 -J-inch plank 12 inches wide is used for the back form, 
and is held in place at the bottom by pegs. The front form consists 
of a plank If by 6 inches, and is held in place by pegs. Before the 
concrete is placed, two sheet-iron plates, cut as shown in the figure, 
are placed in the forms, six feet to eight feet apart. After the con- 
crete for the gutter and the lower part of the curb is placed and 
rammed, a lf-inch plank is placed against these plates and held in 
place by screw clamps (Fig. 86). The upper part of the curb is then 




Fig. 87. Radius Tool. Fig. 88. Inside Angle Tool. 



moulded. When the concrete is set enough to stay in place, the 
front forms and plates are removed, and the surface is treated in the 
same manner as described for the other type of curb. 

255. Cost. The cost of concrete curb will depend upon the 
conditions under which it is made. Under ordinary circumstances, 
the contract price for rectangular curbing 6 inches wide and 24 inches 
deep will be about $0.60 per linear foot; or $0.80 per linear foot for 
curb 8 inches wide and 24 inches deep. Under favorable conditions 
on large jobs, 6-inch curbing can be constructed for $0.40 or $0.45 
per linear foot. These prices include the excavation that is required 
below the street grade. 

The cost of the combined curb and gutter is about 10 to 20 per 
cent more than that of the rectangular curbing. In addition to hav- 
ing a larger surface to finish, the combined curb and gutter requires 
more material, and therefore more work, to construct it. 



MASONRY AND REINFORCED 
CONCRETE 

PART III 



REINFORCED CONCRETE 

GENERAL THEORY OF FLEXURE 
250. Introduction. The theory of flexure in reinforced concrete 
is exceptionally complicated. A multitude of simple rules, formula 1 , 
and tables for designing reinforced-concrete work have been proposed, 
some of which are sufficiently accurate and applicable under certain 
conditions. But the effect of these various conditions should be 
thoroughly understood. Reinforced concrete should not be designed 
by "rule-of-thumb" engineers. It is hardly too strong a statement 
to say that a man is criminally careless and negligent when he at- 
tempts to design a structure on which the safety and lives of people 
will depend, without thoroughly understanding the theory on which 
any formula he may use is based. The applicability of all formulae is 
so dependent on the quality of the steel and of the concrete, and on 
many of the details of the design, that a blind application of a formula 
is very unsafe. Although the greatest pains will be taken to make 
the following demonstration as clear and plain as possible, it will be 
necessary to employ symbols, and to work out several algebraic 
formula 1 on which the rules for designing will be based. The full 
significance of many of the terms mentioned below may not be fully 
understood until several subsequent paragraphs have been studied: 

b = Breadth of concrete beam; 

d = Depth from compression face to center of gravity of the steel; 
fl$— A = Area of the steel; 

p = Ratio of area of steel to area of concrete above the center of 
gravity of the steel, generally referred to as percentage of re- 
inforcement, 

hd> tl 

Copyright, 1908, by American School of Correspondence. 



174 MASONRY AND REINFORCED CONCRETE 

E s = Modulus of elasticity of steel; 

E c = Initial modulus of elasticity of concrete; 

E 
■ft-—- r = ■— = Ratio of the moduli; 

s = Tensile stress per unit of area in steel; 

c = Compressive stress per unit of area in concrete at the outer fibre 
of the beam; this may vary from zero to c'; 
Jltimate compressive stress per unit of a 
stress at which failure might be expected; 
e 9 = Deformation per unit of length in the steel; 
e c = " " " " " in outer fibre of concrete; 

e c ' = " " " " " in outer fibre of concrete when 

crushing is imminent; 
Cc " = Deformation per unit of length in outer fibre of concrete under a 
certain condition (described later); 

o = — — = Ratio of deformations; 

k = Ratio of depth from compressive face to the neutral axis to the 

total effective depth d; 
x = Distance from compressive face to center of gravity of com- 
pressive stresses; 
2 X = Summation of horizontal compressive stresses; 
M = Resisting moment of a section. 

257. Statics of Plain Homogeneous Beams. As a preliminary 
to the theory of the use of reinforced concrete in beams, a very brief 

discussion will be given of 

^ ^^^^ ^^^^^ CJ^^^^^^^ M the statics of an ordinary 

. t- jr— ! B i) ' ? homogeneous beam. Let A B 

ji iuuuiu »• (Fig * 89 ^ represent a beam 

Q I- 2 — carrying a uniformly distrib- 

*^ uted load W; then the beam 

Fig. 89. Beam Carrying Uniformly Dis- IS Subjected to transverse 

tributed Load. ... 

stresses. Let us imagine that 
one-half of the beam is a "free body" in space, and is acted on by 
exactly the same external forces ; we shall also assume the forces C 
and T (acting on the exposed section), which are just such forces as 
are required to keep that half of the beam in equilibrium. 

These forces, and their direction, are represented in the lower 
diagram by arrows. The load W is represented by the series of 
small, equal, and equally spaced vertical arrows pointing downward. 
The reaction of the abutment against the beam is an upward force, 



MASONRY AND REINFORCED CONCRETE 



175 



shown at the left. The forces acting on a section at the center are the 
equivalent of the two equal forces C and T. 

The force C, acting at the top of the section, must act toward 
the left, and there is therefore compression in that part of the section. 
Similarly, the force T is a force acting toward the right, and the fibres 
of the lower part of the beam are in tension. For our present purpose 
we may consider that the forces C and T are in each case the resultant 
of the forces acting on a very large number of "fibres." The stress 
in the outer fibres is of course greatest. At the center of the height, 
there is neither tension nor compression. This is called the neutral 
axis (see Fig. 90). 

Let us consider for simplicity a very narrow portion of the beam, 
having the full length and depth, but so narrow that it includes only 



Neutra] 



Aaa»L!3_ 



t 




Fig. 90. Position of Neutral Axis. 



Fig. 91. Neutral Axis in Narrow Beam. 



one set of fibres, one above the other, as shown in Fig. 91. In the 
case of a plain, rectangular, homogeneous beam, the stresses in the 
fibres would be as given in Fig. 90; the neutral axis would be at the 
center of the height, and the stress at the bottom and the top w r ould 
be equal but opposite. If the section were at the center of the beam, 
with a uniformly distributed load (as indicated in Fig. 89), the shear 
would be zero. 

A beam may be constructed of plain concrete; but its strength 
will be very small, since the tensile strength of concrete is compar- 
atively insignificant. Reinforced concrete utilizes the great tensile 
strength of steel, in combination with the compressive strength of 
concrete. It should be realized that the essential qualities are com- 
pression and tension, and that (other things being equal) the cheap- 
est method of obtaining the necessary compression and tension is the 
most economical. 



176 MASONRY AND REINFORCED CONCRETE 

258. Economy of Concrete for Compression. The ultimate 
compressive strength of concrete is generally 2,000 pounds or over per 
square inch. With a factor of safety of four, a working stress of 500 
pounds per square inch may be considered allowable. We may 
estimate that the concrete costs twenty cents per cubic foot, or $5.40 
per cubic yard. On the other hand, we may estimate that the steel, 
placed in the work, costs about three cents per pound. It will weigh 
480 pounds per cubic foot; therefore the steel costs $14.40 per cubic 
foot, or 72 times as much as an equal volume of concrete or an equal 
cross-section per unit of length. But the steel can safely withstand a 
compressive stress of 16,000 pounds per square inch, which is 32 
times the safe working load on concrete. Since, however, a given 
volume of steel costs 72 times an equal volume of concrete, the cost 
of a given compressive resistance in steel is ^f (or 2.25) times the cost 
of that resistance in concrete. Of course, the above assumed unit- 
prices of concrete and steel will vary with circumstances. The 
advantage of concrete over steel for. compression may be somewhat 
greater or less than the ratio given above, but the advantage is almost 
invariably with the concrete. There are many other advantages in 
addition, which will be discussed later. 

259. Economy of Steel for Tension. The ultimate tensile 
strength of ordinary concrete is rarely more than 200 pounds per 
square inch. With a factor of safety of four, this would allow a 
working stress of only 50 pounds per square inch. This is generally 
too small for practical use, and certainly too small for economical use. 
On the other hand, steel may be used with a working stress of 16,000 
pounds per square inch, which is 320 times that allowable for con- 
crete. Using the same unit-values for the cost of steel and concrete 
as given in the previous section, even if steel costs 72 times as much 
as an equal volume of concrete, its real tensile value economically 
is -Vy (or 4.44) times as great. Any reasonable variation from the 
above unit-values cannot alter the essential truths of the economy 
of steel for tension and of concrete for compression. In a reinforced- 
concrete beam, the steel is placed in the tension side of the beam. 
Usually it is placed from one to two inches from the outer face, with 
the double purpose of protecting the steel from corrosion or fire, and 
also to better insure the union of the concrete and the steel. But the 
concrete below the steel is not considered in the numerical calcu- 



MASONRY AND REINFORCED CONCRETE 



177 




lations. Even the concrete which is between the steel and the neu- 
tral axis (whose position will be discussed later), is chiefly useful in 
transmitting the tension in the steel to the concrete. Although such 
concrete is theoretically subject to tension, and does actually con- 
tribute its share of the tension when the stresses in the beam are 
small, the proportion of the necessary tension which the concrete can 
furnish when the beam is heavily loaded, is so very small that it is 
usually ignored, especially since "such a policy is on the side of safety, 
and also since it greatly simplifies the theoretical calculations and 
yet makes very little difference in the final result. We may therefore 
consider that in a unit-section of the beam, 
as in Fig. 92, the concrete above the neu- 
tral axis is subject to compression, and that 
the tension is furnished entirely by the 
steel. 

2(H). Elasticity of Concrete in Com= 
pression. In computing the transverse 
stresses in a wooden beam or steel I-beam, 
it is assumed that the modulus of elastic- 
ity is uniform for all stresses within the 

elastic limit. Experimental tests have shown this to be so nearly 
true that it is accepted as a mechanical law. This means that if a 
force of 1,000 pounds is required to stretch a bar .001 of an inch, it 
will require 2,000 pounds to stretch it .002 of an inch. Similar tests 
have been made with concrete, to determine the law of its elasticity. 
Unfortunately, concrete is not so uniform in its behavior as steel. 
The results of tests are somewhat contradictory. Many engineers 
have argued that the elasticity is so nearly uniform that it may be 
considered to be such within the limits of practical use. But all 
experimenters who have tested concrete by measuring the propor- 
tional compression produced by various pressures, agree that the 
additional shortening produced by an additional pressure, say of 100 
pounds per square inch, is greater at higher pressures than at low 
pressures. 

A test of this sort may be made substantially as follows: A 
square or circular column of concrete at least one foot long is placed 
in a testing machine. A very delicate micrometer mechanism is 
fastened to the concrete by pointed screws of hardened steel. These 



Fig. l J2. Transmission of- Ten- 
sion in Steel to Concrete. 



178 



MASONRY AND REINFORCED CONCRETE 



points are originally at a known distance apart — say 8 inches. When 
the concrete is compressed, the distance between these points will be 
slightly less. A very delicate mechanism will permit this distance to 
be measured as closely as the ten-thousandth part of an inch, or to 

about TT^rT^r °f tne length. Suppose that the various pressures per 

square inch, and the proportionate compressions, are as given in the 
following tabular form : 



Pressure pee 


Square Inch 


Proportionate Compression 


200 


pounds 


.00010 of 


total 


length 


400 


it 


.00020 " 


a 


ti 


600 


a 


.00032 " 


it 


a 


800 


it 


.00045 " 


it 


tt 


1,000 


tt 


.00058 " 


a 


it 


1,200 


a 


.00062 " 


a 


n 


1,400 


tt 


.00090 " 


a 


tt 


1,600 


tt 


.00112 " 


a 


tt 



£.Q02 



2 
a> 

O.00I 



We may plot these pressures and compressions as in Fig. 93, 
using any convenient scale for each. For example, for a pressure of 
800 pounds per square inch, we select the vertical line which is at the 

horizontal distance 
from the origin O 
of 800, according to 
the scale adopted. 
Scaling off on this 
vertical line the or- 
dinate .00045, ac- 
cording to the scale 
adopted for com- 
pressions, we have 
the position of one 
point of the curve. 
The other points are 
obtained similarly. Although the points thus obtained from the 
testing of a single block of concrete would not be considered suffi- 
cient to establish the law of the elasticity of concrete in compression, 
a study of the curves which may be drawn through the series of 



,CL L 


p. 


1 


^ 


J- 


^ 


5 ■: 


-x< 


/^ 




f-S- 




£ 




J? 




^ 




S ± . 





IOOO 2000 

Compression in concrete — povmds 



Fig. 



Curve of Pressures and Compressions. 



MASONRY AND REINFORCED CONCRETE 179 

points obtained for each of a large number of blocks, shows that 
these curves will average very closely to parabolas that are tangent 
to the initial modulus of elasticity, which is here represented in 
the diagram by a straight line running diagonally across the figure. 

It is generally considered that the axis of the parabola will be a 
horizontal line when the curve is plotted according to this method. 
The position of the vertex of the parabola cannot be considered as 
definitely settled. Professor Talbot has computed the curve as if the 
vertex were at the point of the ultimate compression of the con- 
crete, although he conceded that the vertex might be in an imaginary 
position corresponding to a compression in the concrete higher than 
that which the concrete could really endure. Mr. A. L. Johnson, 
another noted authority, bases his computation of formulae on the 
assumption that the ultimate compressive strength of the concrete 
is two-thirds of the value which would be required to produce that 
amount of compression in case the initial modulus of elasticity were 
the true value for all compressions. In other words, looking at Fig. 
93, if o c is a line representing the initial modulus of elasticity, then, 
if the elasticity were uniform throughout, it would require a force of 
about 2,340 pounds (or d /) to produce a proportionate compression of 
.00132 of the length (represented by o d). Actually that compression 
will be produced when the pressure equals d e, which is J of d /. It 
should not be forgotten that the above numerical values are given 
merely for illustrative purposes. They would, if true, represent a 
rather weak concrete. The following theory is therefore based on the 
assumption that the stress-strain curve is represented by the para- 
bolic curve o e (see Fig 93) ; and that the ultimate stress per square 
inch in the concrete c' is represented by d e, which is J of the com- 
pressive stress that would be required to produce that proportionate 
compression if the modulus of elasticity of the concrete were uniformly 
maintained at the value it has for very low pressures. 

261. Theoretical Assumptions. The theory of reinforced -con- 
crete beams is based on the usual assumptions that : 

(a) The loads are applied at right angles to the axis of the beam. The 
usual vertical gravity loads supported by a horizontal beam fulfil this condition. 

(b) There is no resistance to free horizontal motion. This condition 
is seldom, if ever, exactly fulfilled in practice. The more rigidly the beam is 
held at the ends, the greater will be its strength above that computed by the 
simple theory. Under ordinary conditions the added strength is quite inde- 



ISO 



MASONRY AND REINFORCED CONCRETE 



In Fig. 94 is shown, 
meaning of assumption d. 




terminate; and is not allowed for, except in the appreciation that it adds indef- 
initely to the safely. 

•(c) The concrete and steel stretch together without breaking the bond 
between them. This is absolutely essential. 

(fi) Any section of the beam which is plane before bending is 
plane after bending. 

in a very exaggerated form, the essential 
The section ab c din the unstrained con- 
dition, is changed to the 
plane a! V c' d l when the 
load is applied. The com- 
pression at the top = ad ' = 
b V '. The neutral axis is 
unchanged. The concrete at 
the bottom is stretched an 
amount = c c' = dd! , while 
the stretch in the steel equals 
g g' '. The compression in 
the concrete between the 
neutral axis and the top is 
proportional to the distance 
from the neutral axis. 

In Fig. 95 a is given a side 
view of the beam, with spe- 
cial reference to the deform- 
ation of the fibres. Since 
the fibres between the neu- 
tral axis and the compressive 
face are compressed propor- 
tionally, then, if a a' repre- 
sents the linear compression 
of the outer fibre, the shaded 
lines represent, at the same 
scale, the compression of the intermediate fibres. 

In Fig. 956, m n indicates the stress there would be in the outer 
fibre if the initial modulus of elasticity applied to all stresses. But 
since the force required to produce the compression a a! is proportion- 
ately so much less than that required for the lesser compressions, the 
actual pressure in pounds on the outer fibre may be represented by a 



Fig. 94. 



Plane Section of Beam before and 
after Bending. 



,'Ue'cJ, 






Neutral Axis 



\ 

\ 
\ 
\ 
\ 





T 


i 


v-. - " 


Kd 




^! 


I 




N 


\ c 
\ 
\ 

\ 
\ 


1 




"\ 



Fig. 95. 



h — s- 



Fibre Stresses in Beams. 



MASONRY AND REINFORCED CONCRETE 



181 



line v n, and the pressure on the intermediate fibres by the ordinates 
to the curve v N. 

In Fig. 96, a and b, are shown a pair of figures corresponding with 
those of Fig. 95, except that the compressive deformation of the con- 
crete in the outer fibre a a! is only one-half of the value in Fig. 95. 
But it will require about three-fourths as much pressure to produce 
one-half as much compression. In Fig. 96, v' n' is therefore three- 
fourths of v n in Fig. 95. The student should note that k f here 
differs slightly from k, which means that the position of the neutral 
axis varies with the conditions. 

262. Summation of the Compressive Forces. The summation 
of the compressive forces is evidently indicated by the area of the 




,. Neutral 

■~Kr n 



3c!!r 



Axis 



T 

Kd 

1 



(a.) 

Fig. 96. 



U) 




Fibre Stresses in Beams. 



Fig. 97. Summation of Com- 
pressive Forces. 

shaded portion in Fig. 97. The curve v N is a portion of a parabola. 

The area of the shaded portion between the curve v N and the straight 

line v N, equals one-third of the area of the triangle mN v. The area 

of the triangle v n N = \ c kd. Therefore, for the total shaded area, 

we have: 

Area = \ ckd + % (c — c) \ kd, 

= | kd (q + J c — J c), 

= \ kd (§c + J Co). 

But in this case, c = E t e c ; therefore, 

Area = £ kd (f c '+ £ E c e c ) (9) 

In Fig. 98 has been redrawn the parabola of Fig. 93, in which o 
is the vertex of the parabola. Here c" is the force which would pro- 
duce a compression of e c " provided the concrete could endure such a 
pressure without rupture. If the initial modulus of elasticity applied 
to all stresses, the required force would be the line E c e c ". And c" 
= i E r e " 



182 



MASONRY AND REINFORCED CONCRETE 



It is one of the well-known properties of the parabola that 
abscissae are proportional to the squares of the ordinates, or that 
(in this case): 

k'd :mn::ok :o m 

Transforming to the symbols, we have : 



(c"-c):c" :: (e c "-e c ) 2 :e c "* ; 



c" —c = c" (1 — q) 2 , since — % = q. 
c=c"{l-(l-<2) 2 [ ; 
= c" (2q-q 2 ) ; 
= \ E c e<."(2q —q 2 ), since c"=\ E c e c " ; and also, since e c " = — 

= £ c e c (l-lg). • • ' (10) 

Substituting this value of c in Equation 9, we have: 



Area 



The summation 
of the horizontal 
forces ( 2X ) with- 
in the shaded area, 
is evidently ex- 
pressed by the 
above "area" mul- 
tiplied by the 
breadth of the 
beam (b). There- 
fore, 




IX 



Fig. 98 

= Hi 



Analysis of Compressive Stresses. 
- lq) E c e c bkd (1 1) 



In order to avoid the complication resulting from the attempt 

to develop formulae which are applicable to all kinds of assumptions, 

it will be at once assumed, as previously referred to, that the ultimate 

compressive strength of the concrete is J of the value which would be 

required to produce that amount of compression in case the initial 

modulus of elasticity were the true value for all compressions. 

The proof that q will equal f under these conditions, is perhaps deter- 
mined most easily by computing the ratio of 6 h to q h (see Fig. 98) when o a is 
assumed to be J of o m. In this case, from the properties of the parabola, a b 

i /,' e " 



MASONRY AND REINFORCED CONCRETE 183 

But when o a = % of orri, g h = jj K c e c " = !; E c e c ". 

Therefore c' = § <j h. But when o a = J of <> in, ~ = §. 

Therefore, when c' = $ gh, q = §. 

It has already been shown that c" = J E c e e ff t and also that e c "= 

6 

' . Therefore J E c e c = c"g. It has also been shown that c' = J c", 

or that c" = fc'. Therefore i E c e c =-| c'g. 

Substituting this value in Equation 1 1, we have for the summa- 
tion of the compressive forces above the neutral axis, under such 
conditions: 

IX = %(l-$q)qc'bkd (12) 

Substituting the further condition that q = |, we have: 

IX = ■. 1 v'b kd (13) 

263. Center of Gravity of Compressive Forces. This is also 
called the ccntroid of compression. The theoretical determination of 
this center of gravity is virtually the same as the determination of the 
center of gravity of the shaded area shown in Figs. 96 and 97. The 
general method of determining this center of gravity requires the use 
of differential calculus, and is a very long and tedious calculation. 
But the final result may be reduced to a surprisingly simple form, as 
expressed in the following equation : 

7 7 4 — <7 
12 — 4$ 

Assuming, as explained above, the value of <j = f, this reduces to: 

x = .357 kd (14) 

When q equals zero, the value of x equals .333 kd; and, at the other ex- 
treme, when q 1 , x .375 kd. 

There is, therefore, a very small range of inaccuracy in adopting the 
value of </ = | for all computations. 

2(>4. Position of the Neutral Axis. According to one of the 
fundamental laws of mechanics, the sum of the horizontal tensile 
forces must be equal and opposite to the sum of the compressive 
forces. Ignoring the very small amount of tension furnished by the 
concrete below the neutral axis, the tension in the steel =As = pbds = 
the total compression in the concrete. Therefore, applying Equa- 
tion 1 1, 

pbds = HI - h <l) He *c k b d 
I But s = E a e a ; therefore, 
p E s e 8 = J (1 -|5)£ c e c k 



184 MASONRY AND REINFORCED CONCRETE 



El 

But ^- = r; and by proportional triangles, as shown in Fig. 96, 

e c _ e s k 

kd ~ d-kd ' ° r €c ~ €a pTjfc ' 

Making these substitutions, we have : 

vt- id-ia)^ (IS) 

Solving this quadratic for A;, we have : 



^(l-*9) (W<?) 2 (1-43) 

Equation 16 is a perfectly general equation which depends for its 
accuracy only on the assumption that the law of compressive stress 
to compressive strain is represented by a parabola. The equation 
shows that k, the ratio determining the position of the neutral axis, 
depends on three variables — namely, the percentage of the steel (p), 
the ratio of the moduli of elasticities (r), and the ratio of the deforma- 
tions in the concrete (q). These must all be determined more or less 
accurately before we can know the position of the neutral axis. 

On the other hand, if it were necessary to work out Equation 16, 
as well as many others, for every computation in reinforced concrete, 
the calculations would be impracticably tedious. Fortunately the 
extreme range in k for any one ratio of moduli of elasticities, is only 
a few per cent, even when q varies from to 1. We shall therefore 
simplify the calculations by using the constant value q = § , as ex- 
plained above. 

Substituting q = § in Equation 16, we have: 



n 



. 81" 9 (\*7\ 

p r H — p 2 r 2 — —v r \ m ' ) 

49 7 



The various values for the ratio of the moduli of elasticity (r) are 
discussed in the succeeding section. The values of A- for various 
values of r and p, and for the uniform value of q = f , have been com- 
puted in the following tabular form. Five values have been chosen 
for r, in conjunction with nine values of p, varying by 0.2 per cent 
and covering the entire practicable range of p, on the basis of which 
values k has been worked out in the tabular form. Usually the value 
of k can be determined directly from the table. By interpolating 
between two values in the table, any required value within the limits 
of ordinary practice can be determined with all necessary accuracy. 



MASONRY AND REINFORCED CONCRETE 



185 



TABLE XIII 
Values of k for Various Values of r and p (Parabolic Formulae) 





P 


;• 


.020 


.018 


.016 


.014 


.012 


.010 


.008 


.006 


.004 


10 


.505 


.487 


.468 


.446 


.422 


.395 


.362 


.323 


.274 


12 


.536 


.517 


.497 


.475 


.450 


.422 


.388 


.348 


.295 


15 


.574 


.555 


.535 


.513 


.488 


.458 


.422 


.379 


.323 


20 


.623 


.604 


.583 


.561 


.535 


.505 


.468 


.421 


.362. 


40 


.736 


.718 


.700 


.678 


.654 


.623 


.584 


.535 


.468 



265. Ratio of Moduli. Theoretically there is an indefinite 
number of values of r, the ratio of the moduli of elasticity of the steel 
and the concrete. The modulus for steel is fairly constant at about 
29,000,000 or 30,000,000. The value of the initial modulus for con- 
crete varies according to the quality of the concrete, from 1,500,000 to 
3,000,000 for stone concrete. An average value for cinder concrete is 
about 750,000. Some experimental values for stone concrete have 
fallen somewhat lower than 1,500,000, while others have reached 
4,000,000 and even more. We may probably use the following values 
with the constant value of 29,000,000 for the steel. 

TABLE XIV 
Modulus of Elasticity of Some Grades of Concrete 



Kind of Concrete 


Mixture 


E, 


r 




1:2:5 
1:6:12 
1:3:5 
1:2:4 


750,000 
1,450,000 
2,400,000 
2,900,000 


40 




20 


it a 


12 


tt tt 


10 







The value given above for 1:G:12 concrete is mentioned only 
because the value r = 20 is sometimes used with the weaker grades of 
concrete, and the value of approximately 1,450,000 for the elasticity 
of such concrete has been found by experimenters. The use of such 
a lean concrete is hardly to be recommended, because of its unrelia- 
bility. Considering the variability in cinder concrete, the even value 
of r = 40 is justifiable, rather than the precise value 38.67. 

266. Percentage of Steel. The previous calculations have been 
made as if the percentage of the steel might be varied almost in- 



186 MASONRY AND REINFORCED CONCRETE 

definitely. While there is considerable freedom of choice, there are 
limitations beyond which it is useless to pass; and there is always a 
most economical percentage, depending on the conditions. We have 
already determined that : 

e c k 

e s 1 — k ' 

Q 

But e c = — - ; (see Equation 10), and 

e s = ^— ; therefore, 



e, 



c E s c r k 



e s sE c (l-\q) s(l-ig) 1-fc 
Solving for k, we have : 

7. cr 

' ~ cr + s(l-ig) ' 
Using as before the value of q — f , the equation becomes: 

cr + .667 s* 

Using the same value of q in Equation 15, and solving for p, we have: 

7 fc 2 
pr ~ 18(l-/c)* 

Substituting the above value of k in this equation, we have, after consid- 
erable reduction: 

p-±t C -L (18) 

F 12 s (cr + ,667s) y 

The above equation shows that we cannot select the percentage 
of steel at random, since it evidently depends on the selected stresses 
for the steel and concrete, and also on the ratio of their moduli. For 
example, consider a high-grade concrete (1:2:4) whose modulus of 
elasticity is considered to be 2,900,000, and which has a limiting com- 
pressive stress of 2,700 pounds [c f ), which we may consider in con- 
junction with the limiting stress of 55,000 pounds in the steel. The 
values of c, s, and r are therefore 2,700, 55,000, and 10 respectively. 
Substituting these values in Equation 18, we compute p = .012. 

Example. What percentage of steel would be required for 
ordinary stone concrete, with r = 15, c =2,000, and s = 55,000? 
Ans. . 95 per cent. 

267. Resisting Moment. The moment which resists the action 
of the external forces is evidently measured by the product of the 
distance from the center of gravity of the steel to the centroid of 
compression of the concrete, times the total compression of the con- 



MASONRY AND REINFORCED CONCRETE 187 

crete, or, otherwise, times the tension in the steel. The compression 
in the concrete and the tension in the steel are equal, and it is there- 
fore only a matter of convenience to express this product in terms of 
the tension in the steel. Therefore, adopting the notation already 
mentioned, we may write the formula: 

M = As (d-x) (19) 

But since the computations are frequently made in terms of the dimen- 
sions of the concrete and of the percentage of the reinforcing steel, 
it may be more convenient to write the equation : 

M = pbds(d-x) (20) 

From Equation 12 we have the total compression in the concrete. 
Multiplying this by the distance from the steel to the centroid of 
compression (d — x), we have another equation for the moment: 



9 ,. 1 



(1 



\q) qc'bkd(d-x) (21) 



• u 8 v 3 

This equation is perfectly general, except that it depends on the 
assumption as to the form of the stress-strain diagram as described in 
Article 260. On the assumption that q = J for ultimate stresses in 
the concrete, the equation becomes : . 

M =^c'bkd(d-x) (22) 

When the percentage of steel used agrees with that computed from 

Equation 18, then Equations 20 and 22 will give identically the 

same results ; but when the percentage of steel is selected arbitrarily, 

as is frequently done, then the proposed section should be tested by 

both equations. When the percentage of steel is larger than that 

required by Equation 18, the concrete will be compressed more than 

is intended before the steel attains its normal tension. On the other 

hand, a lower percentage of steel will require a higher unit-tension 

in the steel before the concrete attains its normal compression. When 

the discrepancy between the percentage of steel assumed and the 

true economical value is very great, the stress in the steel (or the 

concrete) may become dangerously high when the stress in the other 

element (on which the computation may have been made) is only 

normal. 

268. Example 1. What is the ultimate resisting moment of a concrete 
beam made of 1:3:5 concrete, which is 7 inches wide, 10 inches deep to the 



188 MASONRY AND REINFORCED CONCRETE 

reinforcement, and which uses 1.2 per cent of reinforcement? The concrete 
is supposed to have a ratio for the moduli of elasticity (r) of 15. The ultimate 
strength of the concrete (c') is assumed as 2,000. 

Answer. From Table XIII, p = .012, and r = 15, k = .490; 
x = .357 Jed = .175 d; d — x = .825 d. From Equation 22 we have: 

M = — X 2,000 X .490 X 7 X 10 X 8.25=330,137 inch-pounds. 

The total compression in the concrete is the continued product of 
all the factors except the last, and equals 40,017. But this equals the 
tension in the steel, whose area = pbd = .012 X 7 X 10 = .84 
square inch. Therefore the unit-stress in the steel would equal 
40,017 -r- .84 = 47,640 pounds per square inch. This is considerably 
less than the usual ultimate of 55,000, and shows that the percentage 
of stee.1 is considerably in excess of the normal value. 
From Equation 20, assuming s = 55,000, we have : 

M =.012 X 7 X 10 X 55,000 X 8.25 = 372,900 inch-pounds. 

If the beam were actually stressed with this moment, the total com- 
pression in the concrete would equal 372,900 -f 8.25 = 45,200 
pounds. From Equation 13 we have: 

45,200 = ^-c'bkd= -£-c' X 7 X .490 X 10. 

Solving for c', 

c' = 45,200 -=- 20.008 = 2,205 pounds, 

which is considerably more than that assumed — 2,000. 

The practical interpretation of the above is that if the beam 
is tested by Equation 22, indicating an ultimate moment of 330,137 
inch-pounds, and the actual* proposed loading, multiplied by its 
factor of safety, does not have a moment which exceeds this, value, 
the compression in the concrete will not be more than 2,000 pounds 
per square inch, while the tension in the steel will be not greater 
than 47,640 pounds per square inch {ultimate value), which is safe 
but uneconomical. On the other hand, if Equation 20 were employed, 
indicating an ultimate moment of 372,900 pounds, and the ultimate 
loading of the beam seemed to require this moment, the steel would 
be all right, but the concrete would have an ultimate compression of 
2,205 pounds, which would be dangerous for that grade of concrete. 
Therefore, as a general rule, whenever the percentage of steel has been 
assumed, both equations (20 and 22) should be tested. The lowest 



MASONRY AND REINFORCED CONCRETE 189 

ultimate moment should be the limit which should not be exceeded 
by the ultimate moment of the actual loading, for the use of the 
higher value will mean an excessive stress in either the concrete or 
the steel. 

Example 2. What will be the ultimate resisting moment of a 5-inch 
slab made of a high quality of concrete (1:2:4), using the most economical 
percentage of steel? 

Answer. For this quality of concrete, r = 10; the ultimate 
compressive strength of the concrete is 2,700; and the ultimate 
tension in the steel is assumed at 55,000. Substituting these values 
in Equation 18, we find that the economical percentage of steel is 
1.21. Interpolating this value of p in Table XIII, considering that 
r = 10, we have k = .424. Substituting this value of k in Equation 
14, we find that x = .151 d. In the case of the 5-inch slab, we shall 
assume that the center of gravity of the steel is placed 1 inch from 
the bottom of the slab. Therefore d = 4 inches. For a slab of 
indefinite width, we shall assume that b = 12 inches. Therefore our 
computed value for the ultimate resisting moment gives the moment 
of a strip of the slab one foot wide, and the computed amount of the 
steel is the amount of steel per foot of width of the slab. 

Substituting these various values in Equation 20, we find as the 
value of the ultimate resisting moment: 

M = .0121 X 12 X 4 X 55,000 X .849 X 4 - 108,482 inch-pounds 

The area of steel required for each foot of width is: 

.4 = .0121 X 12 X 4 = .5808 square inch. 

This equals .0484 square inch per inch of width. Since a J-inch 

square bar has an area of .25 square inch, we may provide the rein- 

25 
forcement by using J-inch square bars spaced n = 5.17 inches, 

or, say, 5 J inches. 

Example 3. A very instructive comparison may be made by 
considering a 5-inch slab with d = 4 inches, but made of 1:3:5 con- 
crete. In this case we call r = 12; c = 2,000; and s (as before) = 
55,000. By the same method as before, we obtain p = .0084; k = 
.395; and therefore x = .141 d. Substituting these values in Equa- 
tion 20, we have : 

M - .0084 X 12 X 4 X 55,000 X .859 X 4= 76,197 inch-pounds. 



190 MASONRY AND REINFORCED CONCRETE 

The area of steel per foot of width is: 

A = .0084 X 12 X 4 = .4032 square inch. 

This would require J-inch square bars spaced 7.33 inches. Although 
the amount of steel required in this slab is considerably less than 
was required in the previous case, the ultimate moment of the slab 
is also very much less. In fact the reduction of strength is very 
nearly in proportion to the reduction in the amount of steel. There- 
fore, it must be observed that, although the percentage of steel used 
with high-grade concrete is considerably higher, the thickness of the 
concrete will be considerably less; and in spite of the fact that the 
percentage of steel may be higher, its absolute amount for a slab of 
equal strength may be approximately the same. 

Example 4. Another instructive principle may be learned by 
determining the required thickness of a slab made of 1:3:5 concrete, 
which shall have the same ultimate strength as the high-grade con- 
crete mentioned in example 2. In other words, its ultimate moment 
per foot of width must equal 108,482 inch-pounds. The values of 
r, c, and s are the same as in example 3, and therefore the value of 
p must be the same as in example 3; therefore p — .0084. Since 
r and p are the same as in example 3, k again equals .395, and there- 
fore x = .141 d. We therefore have from Equation 20: 

M = 108,482 = .0084 X 12 X d X 55,000 X .859 X d. 

Solving this equation for d, we find d 2 = 22.78; and d = 4.77. The 
area of the steel A = pbd = .0084 X 12 X 4.77 = .481. This is 
considerably less than the area of steel per foot of width as computed 
in example 2 for a slab of equal strength. On the other hand, the 
slab of 1:3:5 concrete will require about 15 per cent more concrete. 
It will also weigh about 10 pounds per square foot more than the 
thinner slab, which will reduce by that amount the permissible live 
load. The determination of the relative economy of the two kinds 
of concrete will therefore depend somewhat on the relative price 
of the concrete and the steel. The difference in the total cost of the 
two methods is usually not large; and abnormal variation in the 
price of cement or steel may be sufficient to turn the scale one way or 
the other. 

269. Determination of Values for Frequent Use. The above 
methods of calculation may be somewhat simplified by the determi- 



MASONRY AND REINFORCED CONCRETE 191 

nation, once for all, of constants which are in frequent use. For 
example, a very large amount of work is being done, using 1:3:5 
concrete. Sometimes engineers will use the formula? developed on 
the basis of 1:3:5 concrete, even when it is known that a richer 
mixture will be used. Although such a practice is not economical, 
the error is on the side of safety; and it makes some allowance for the 
fact that a mixture which is nominally richer may not have any 
greater strength than the values used for the 1:3:5 mixture, on 
account of defective workmanship or inferior cement or sand. Some 
of the constants for use with 1:3:5 mixture and 1:2:4 mixture 
will now be worked out. 

For the 1:3:5 mixture, r = 12; c = 2,000; and we shall assume 
s = 55,000. On the basis of such values, the economical percentage 
of steel is .84 per cent. Under these conditions, k will always be 
.395; and x will equal .141 d. Therefore the term (d — x) will 
always equal .859 d, or, say, .86 d, which is close enough for a working 
value. Since the above values for c and s represent the ultimate 
values, the resulting moment is the ultimate moment, which we shall 
call M Q . Therefore, for 1:3:5 concrete, we have the constant 
values : 

M = .0084 Xbd X 55,000 X .86d 

= 397 fed 2 > ( 23) 

A = .0084 bd) K J 

(d-x)= .8<5d 

Similarly we can compute a corresponding value for 1:2 :4 concrete, 
using the values previously allowed for this grade: 

M = .565 bd 2 I (2A\ 

A = .0121 bd) • • • -V 7 

(d-x) = .86d 

Numerical Example. A flooring with a live-load capacity of 150 pounds 
per square foot, is to be constructed on I-beams spaced 6 feet center to center, 
using 1:3:5 concrete. What thickness of slab will be required, and how much 
steel must be used? 

Answer. Using the approximate estimate, based on experience, 
that such a slab will weigh about 50 pounds per square foot, we can 
compute the ultimate load by multiplying the live load, 150, by four, 
and the dead load, 50, by two, and obtain a total ultimate load of 
700 pounds per square foot. A strip 1 foot wide and 6 feet long 



192 MASONRY AND REINFORCED CONCRETE 



(between the beams) will therefore carry a total load of 700 X 6 = 
4,200 pounds. Considering this as a simple beam, we have : 

M W ° l 4,200 X 6 X 12 Q7snn . , . 

u = ~5 — — o = 37,800 inch-pounds. 

o o 

Placing this numerical value of M = 397 b d 2 , as in Equation 23, we 

have 37,800 = 397 b d 2 . In this case, b = 12 inches. Substituting 

this value of b, we solve for d 2 , and obtain d 2 = 7.93, and d = 2.82 

inches. Allowing an extra inch below the steel, this will allow us to 

use a 4-inch slab. Theoretically we could make it a little less. 

Practically this figure should be chosen. The required steel, from 

Equation 23, equals .0084 bd. Taking b — 1, we have the required 

steel per inch of width of the slab = .0084 X 2.82 = .0237 square 

inch. If we use ^-inch square bars which have a cross-sectional area 

25 
of .25 square inch, we may space the bars n = 10 inches. This 

reinforcement could also be accomplished by using f-inch square bars, 

which have an area of .1406. The spacing mav therefore be ' = 

r & J .0237 

6.0 inches. As referred to later, there should also be a few bars laid 
perpendicular to the main reinforcing bars, or parallel with the I- 
beams, so as to prevent shrinkage. The required amount of this 
steel is not readily calculable. Since the I-beams are 6 feet apart, if 
we place two lines of f-inch square bars spaced 2 feet apart, parallel 
with the I-beams, there will then be reinforcing steel in a direction 
parallel with the I-beams at distances apart not greater than 2 feet, 
since the I-beams themselves will prevent shrinkage immediately 
around them. 

270. Straight=Line Formulae. The working unit-compressions 
for even the best grade of concrete are seldom allowed to exceed 600 
pounds per square inch. An inspection of Fig. 93 will show that the 
curve from the point o to the point indicating a pressure of 600 
pounds, although really a parabola, is so nearly a straight line that 
there is but little error in considering it to be straight. On this 
account, many formulae for the strength of reinforced concrete have 
been developed on the basis of a uniform modulus of elasticity for the 
concrete. This is virtually the same as assuming that q equals zero 
in Equation 16. The other equations which are derived from equa- 
tions involving q, must also be correspondingly modified. 



MASONRY AND REINFORCED CONCRETE 



193 



Adopting the same notation as in Article 25(5, we may say that 
the triangle mnN in Fig. 97 represents the compressive forces; that 
the area of the triangle measures the summation of those forces; and , 
assuming that in this case c = mn, the summation is: 



IX = -cbkd . 



(25) 



The center of gravity of the triangle, which is the centroid of com- 
pression of the concrete, is at ^ of the height of the triangle (led) from 
the compression face of the concrete. The same value is obtained by 
making q = in the equation above Equation 14, which gives us: 



x = ~kd 



Making q = in Equation 16, we have: 

k ~ ^2pr + p 2 r 2 



pr 



(26) 



(27) 



From this equation we may deduce Table XV, which corresponds to 
Table XIII. 

TABLE XV 

Value of k for Various Values of r and p 

(Straight=Line Formulae) 





P 


r 


.020 


.018 


.016 


.014 


.012 


.010 


.008 


.006 


.004 


.003 


10 


.464 


.446 


.427 


.407 


.385 


.358 


.328 


.292 


.246 


.216 


12 


.493 


.476 


.457 


.436 


.412 


.385 


.353 


.314 


.266 


.235 


15 


.531 


.513 


.493 


.471 


.446 


.418 


.384 


.343 


.291 


.258 


20 


.580 


.562 


.542 


.519 


.493 


.463 


.428 


.384 


.328 


.292 


40 


.698 


.679 


.659 


.637 


.611 


.579 


.542 


.493 


.428 


.384 



k = 



From an equation in Article 266, by calling q = 0, we may write 
. By making q = in Equation 15, we may write pr = 



cr + - s ' 



1 h 



l-jfc 



By eliminating k from these two equations, we may write: 



1 c cr 



2 s (cr + s) 



(28) 



The similarity of this equation to Equation 18 is readily apparent, 
the difference being due only to the elimination of the effect of q. 



194 MASONRY AND REINFORCED CONCRETE 

The moment of resistance of a beam equals the total tension in 
the steel, or the total compression in the concrete (which are equal), 
times (d — x). Therefore we have the choice of two values (as 
before) : 

M c = 5 cbkd (d-x) /^N 

M s = As (d — x) = pbds (d — x) J 

If the economical percentage p has already been determined from 
Equation 28, then either equation may be used, as most convenient, 
since they will give identical results. If the percentage has been 
arbitrarily chosen, then the least value must be determined, as was 
described in Article 267. 

271. Determination of Values for Frequent Use. For 1:3:5 
concrete, using as before r = 12, and with a working value for c = 
500, and s = 16,000, we find from Equation 28 that the economical 
percentage of steel equals : 

1_500. 500 X 12 

p 2 16,000 (500 X 12 + 16,000) 

From Table XV we find by interpolation that, for r = 12, and p = 
.0043, k = .273. Then (see Equation 26): 

x = -kd = .091d; and (d-x) = .909^. 
o 

Substituting these values in either formula of Equation 29, we have: 

M = 62 bd 2 . 

The percentage of steel computed from Equation 28 has been 
called the most economical percentage, because it is the percentage 
which will develop the maximum allowed stress in the concrete and 
the steel at the same time, or by the loading of the beam to some 
definite maximum loading. The real meaning of this is best illus- 
trated by a numerical example using another percentage. Assume 
that the percentage of steel is exactly doubled, or that p = 2 X .0043 
= .0086. From Table XV, for r = 12, and p = .0086, we find 
k =.362; x =. 121c/; and (d — x) = .879c/. Substituting these values 
in both forms of Equation 29, we have: 

M c = 80 bd 2 ; and, 
M, = 121 bd 2 . 



MASONRY AND REINFORCED CONCRETE 195 

The interpretation of these two equations, and also of the equation 
found above (J/ = 02 bd 2 ), is as follows: Assume a beam of definite 
dimensions b and d, and made of concrete whose modulus of elasticity 
is T V that of the modulus of elasticity of the reinforcing steel; assume 
that it is reinforced with steel having a cross-sectional area = .0043 
bd. Then, when it is loaded with a load which will develop a moment 
of 62 bd 2 , the tension in the steel will equal 10,000 pounds per square 
inch, and the compression in the concrete will equal 500 pounds per 
square inch at the outer fibre. Assume that the area of the steel is 
exactly doubled. One effect of this is to lower the neutral axis (k is 
increased from .273 to .362), and more of the concrete is available for 
compression. The load may be increased about 29 per cent, or until 
the moment equals 80 bd 2 , before the compression in the concrete 
reaches 500 pounds per square inch. Under these conditions the 
steel has a tension of about 10,600 pounds per square inch, and its 
full strength is not utilized. If the load were increased until the 
moment was 121 bd 2 , then the steel would be stressed to 16,000 pounds 
per square inch, but the concrete would be compressed to over 750 
pounds, which would of course be unsafe with such a grade of con- 
crete. If the compression in the concrete is to be limited to 500 
pounds per square inch, then the load must be limited to that which 
will give a moment of 80 bd 2 . Even for this the steel is doubled in 
order to increase the load 29 per cent. Whether this is justifiable, 
depends on several circumstances — the relative cost of steel and con- 
crete, the possible necessity for keeping the dimensions of the beam 
within certain limits, etc. Usually a much larger ratio of steel than 
0.43 per cent is used; 1.0 per cent is far more common; but when 
such is used, it means that the strength of the steel cannot be 
fully utilized unless the concrete can stand high compression. A 
larger value of r will indicate higher values of /,-, which will indicate 
higher moments; but r cannot be selected at pleasure. It depends 
on the character of the concrete used; and, with E s constant, a 
large value of r means a small value for E c , which also means a small 
value for c, the permissible compression stress. Whenever the per- 
centage of steel is greater than the economical percentage, as is usual, 
then the upper of the two formulas of Equation 29 should be used. 
When in doubt, both should be tested, and that one giving the lower 
moment should be used. 



196 



MASONRY AND REINFORCED CONCRETE 



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MASONRY AND REINFORCED CONCRETE 197 

Using p = .0075, and r = 12, we have k = .343; x — .114c?; 
and (d — x) = .886 d. Then, since p is greater than the economical 
value, we use the upper formula of Equation 29, and have: 

M = 76 bd 2 (30) 

272. Example 1. What is the working moment for a slab with 5-inch 
thickness to the steel, the concrete having the properties described above? 

Answer. Calling & = 12 inches, M = 76 X 12 X 25 = 22,800 
inch-pounds, the permissible moment on a section 12 inches wide. 

Example 2. A slab having a span of 8 feet is to support a load of 150 
pounds per square foot. The concrete is to be as described above, and the 
percent ago of stool is to be 0.75. What is the required thickness (/ of the steel? 

j I nswer. A strip 12 inches wide has an area of 8 square feet, and 
carries a load of 1,200 pounds. The moment = J Wl = \ X 1,200 
X 96 = 14,400 inch-pounds. For a strip 12 inches wide, b = 12 
inches, and M = 76 X 12 X d 2 = 912tf = 14,400; d 2 = 15.79; d 
= 3.97 inches — or, say, 4 inches. 

273. Table for Slab Computation. The necessity of very fre- 
quently computing the required thickness of slabs, renders very 
useful a table such as is shown in Table XVI, which has been worked 
out on the basis of 1:3:5 concrete, and computed by solving Equation 
23 for various thicknesses d, and for various spans L varying by 
single feet. It should be noted that the loads as given are ultimate 
loads per square foot, and that they therefore include the weight of 
the slab itself, which must be multiplied by its factor of safety, which 
is usually considered as 2. 

For example, in the numerical case of Article 269, we computed 
that there would be a total load of 700 pounds on a span of 6 feet. 
In the column headed 6, we find 794 on the same line as the value of 
3.0 in the column d. This shows that 3.0 is somewhat excessive for 
the value of d. We computed its precise value to be 2.82. On the 
same line, we find under "Spacing of Bars," that f-inch square bars 
spaced 7)\ inches will be sufficient. In the above more precise calcu- 
lation, we found that the bars could be spaced 6 inches apart, as was 
to be expected, since the computed ultimate load is considerably less 
than the nearest value found in the table. 

Example 1. What is the ultimate load that will be carried by a 5-inch 
slab on a span of 10 feet, using 1:3:5 concrete? 



198 MASONRY AND REINFORCED CONCRETE 

Answer. The 5 inches here represents the total thickness, and 
we shall assume that the effective thickness (d) is 1 inch less. There- 
fore d = 4 inches. On the line opposite d = 4 in Table XVI, and 
under the column L = 10, we have 508, which gives the ultimate 
load per square foot. A 5-inch slab will weigh approximately 60 
pounds per square foot, allowing 12 pounds per square foot per inch 
of thickness. Using a factor of 2, we have 120 pounds, which, sub- 
tracting from 508, leaves 388 pounds; dividing this by 4, we have 97 
pounds per square foot as the allowable working load. Such a load 
is heavier than that required for residences or apartment houses. It 
would do for an office building. 

Example 2. The floor of a factory is to be loaded with a live load of 
300 pounds per square foot, the slab to be supported on beams spaced 8 feet 
apart. What must be the thickness of the floor-slab ? 

Answer. With 1,200 pounds per square foot ultimate load for 
the live load alone, we notice in Table XVI, under L = 8, that 1,241 
is opposite to d = 5. This shows that it would require a slab nearly 
6 inches thick to support the live load alone. We shall therefore add 
another half-inch as an estimated allowance for the weight of the 
slab; and, assuming that a 6J-inch slab having a weight of 78 pounds 
per square foot will do the work, we multiply 300 by 4, and 78 by 2, 
and have 1,356 pounds per square foot as the ultimate load to be 
carried. Under L = 8, in Table XVI, we find that 1,356 comes 
between 1,241 and 1,501, showing that a slab with an effective thick- 
ness d of about 5J inches will have this ultimate carrying capacity. 
The total thickness of the slab should therefore be about 6} inches. 
The table also shows that ^-inch bars spaced about 5| inches apart 
will serve for the reinforcement. We might also provide the rein- 
forcement by f-inch square bars spaced a little over 3 inches apart; 
but it would probably be better policy to use the half-inch bars, 
especially since the f-inch bars will cost somewhat more per pound. 

274. Practical Methods of Spacing Slab Bars. It is too much 
to expect of workmen that bars will be accurately spaced when their 
distance apart is expressed in fractions of an inch. But it is a com- 
paratively simple matter to require the workmen to space the bars 
evenly, provided it is accurately computed how many bars should be 
laid in a given width of slab. For example, in the above case, a 
panel of the flooring which is, say, 20 feet wide, should have a definite 



MASONRY AND REINFORCED CONCRETE 199 

number of bars; 20 feet = 240 inches, and 240 4- 5.75 = 41.7. We 
shall call this 42, and instruct the workmen to distribute 42 bars 
equally in the panel 20 feet wide. The workmen can do this without 
even using a foot-rule, and can adjust them to an even spacing with 
sufficient accuracy for the purpose. 

275. Table for Computation of Simple Beams. In Table XVII 
has been computed for convenience the ultimate total load on rec- 
tangular beams made of average concrete (1:3:5) and with a width 
of 1 inch. For other widths, multiply by the width of the beam. 
Since M — J W l; and since by Equation 23, for this grade of con- 
crete, M = 397 b d 2 ; and since for a computation of beams 1 inch 
wide, b = 1 , we may write \ W l = 397 d 2 . For I we shall substitute 
12 L. Making this substitution and solving for W , we have W = 
265 d 2 -T- L. Since b = 1, A, the area of steel per inch of width 
of the beam = .0084 d. 

Example. What is the ultimate total load on a simple beam having a 
depth of 16 inches to the reinforcement, 12 inches wide, and having a span of 
20 feet? 

Answer. Looking in Table XVII, under L = 20, and opposite 
d = 16, we find that a beam 1 inch wide will sustain a total load of 
3,392 pounds. For a width of 12 inches, the total ultimate load will 
be 12 X 3,392 =•= 40,704 pounds. At 144 pounds per cubic foot, the 
beam will weigh 3,840 pounds. Using a factor of 2 on this, we shall 
have 7,680 pounds, which, subtracted from 40,704, gives 33,024. 
Dividing this by 4, we have 8,256 lbs. as the allowable live load on 
such a beam. 

276. Resistance to the Slipping of the Steel in the Concrete. 
The previous discussion has considered merely the tension and com- 
pression in the upper and lower sides of the beam. A plain, simple 
beam resting freely on . two end supports, has neither tension nor 
compression in the fibres at the ends of the beam. The horizontal 
tension and compression, found at or near the center of the beam, 
entirely disappear by the time the end of the beam is reached. This 
is done by transferring the tensile stress in the steel at the bottom of 
the beam, to the compression fibres in the top of the beam, by means 
of the intermediate concrete. This is, in fact, the main use of the 
concrete in the lower part of the beam. 

It is therefore necessary that the bond between the concrete and 



200 



MASONRY AND REINFORCED CONCRETE 





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MASONRY AND REINFORCED CONCRETE 201 

the steel shall be sufficiently great to withstand the tendency to slip. 
The required strength of this bond is evidently equal to the difference 
in the tension in the steel per unit of length. For example, suppose 
that we are considering a bar 1 inch square in the middle of the length 
of a beam. Suppose that the bar is under an actual tension of 
15,000 pounds per square inch. Since the bar is 1 inch square, the 
actual total tension is 15,000 pounds. Suppose that, at a point 1 
inch beyond, the moment in the beam is so reduced that the tension 
in the bar is 14,900 pounds instead of 15,000 pounds. This means 
that the difference of pull (100 pounds) has been taken up by the 
concrete. The surface of the bar for that length of one inch, is four 
square inches. This will require an adhesion of 25 pounds per square 
inch between the steel and the concrete, in order to take up this 
difference of tension. The adhesion between concrete and plain 
bars is usually considerably greater than this, and there is therefore 
but little question about the bond in the center of the beam. But 
near the ends of the beam, the change in tension in the bar is far 
more rapid, and it then becomes questionable whether the bond is 
sufficient. 

Although there is no intention to argue the merits of any form 
of patented bar, this discussion would not be complete without a 
statement of the arguments in favor of deformed bars, or bars with 
a mechanical bond, instead of plain bars. The deformed bars have 
a variety of shapes; and since they are not prismatic, it is evident that, 
apart from adhesion, they cannot be drawn through the concrete 
without splitting or crushing the concrete immediately around the 
bars. The choice of form is chiefly a matter of designing a form 
which will furnish the greatest resistance, and which at the same time 
is nctf unduly expensive to manufacture. Of course, the deformed 
bars are necessarily somewhat more expensive than the plain bars. 
The main line of argument of those engineers who defend the use of 
plain bars, may be summed up in the assertion that the plain bars are 
"good enough," and that, since they are less expensive than deformed 
bars, the added expense is useless. The arguments in favor of a 
mechanical bond, and against the use of plain bars, are based on three 
assertions : 

First: It is claimed that tests have apparently verified the 
a-ssertion that the mere soaking of the concrete in water for several 



202 MASONRY AND REINFORCED CONCRETE 

months is sufficient to reduce the adhesion from \ to §. If this con- 
tention is true, the adhesion of bars in concrete which is likely to be 
perpetually soaked in water, is unreliable. 

Second: Microscopical examination of the surface of steel, and 
of concrete which has been moulded around the steel, shows that the 
adhesion depends chiefly on the roughness of the steel, and that the 
cement actually enters into the microscopical indentations in the 
surface of the metal. Since a stress in the metal even within the 
elastic limit necessarily reduces its cross-section somewhat, the so- 
called adhesion will be more and more reduced as the stress in the 
metal becomes greater. This view of the case has been verified by 
recent experiments by Professor Talbot, who used bars made of tool 
steel in many of his tests. These bars were exceptionally smooth; 
and concrete beams reinforced with these bars failed generally on 
account of the slipping of the bars. Special tests to determine the 
bond resistance, showed that it was far lower than the bond resistance 
of ordinary plain bars. 

Third: There is evidence to show that long-continued vibration, 
such as is experienced in many kinds of factory buildings, etc., will 
destroy the adhesion during a period of years. Some failures of 
buildings and structures which were erected several years ago, and 
which were long considered perfectly satisfactory, can hardly be 
explained on any other hypothesis. Owing to the fact that there are 
comparatively few reinforced-concrete structures which have been 
built for a very long period of years, positive information as to the 
durability and permanency of adhesion is lacking. It must be con- 
ceded, however, that comparative tests of the bond between concrete 
and steel when the bars are plain and when they are deformed (the 
tests being made within a few weeks or months after the concrete is 
made), have comparatively little value as an indication of what that 
bond will be under some of the adverse circumstances mentioned 
above, which are perpetually occurring in practice. Non-partisan 
tests have shown that, even under conditions which are most favor- 
able to the plain bars, the deformed bars have an actual hold in the 
concrete which is from 50 to 100 per cent greater than that of plain 
bars. It is unquestionable that age will increase rather than diminish 
the relative inferiority of plain bars. 

277. Computation of the Bond Required in Bars. From 



MASONRY AND REINFORCED CONCRETE 203 

Equation 19 we have the formula that the resisting moment at any 
point in the beam equals the area of the steel, times the unit tensile 
stress in the steel, times the distance from the steel to the centroid of 
compression of the steel, which is the distance d — x. We may com- 
pute the moment in the beam at two points at a unit-distance apart. 
The area of the steel is the same in each equation, and d — x is 
substantially the same in each case; and therefore the difference of 
moment, divided by (d — x), will evidently equal the difference in the 
unit-stress in the steel, times the area of the steel. To express this in 
an equation, we may say, denoting the difference in the moment by 
d M 3 and the difference in the unit-stress in the steel by d s : 

dM 
(d-x) 

But A X d s is evidently equal to the actual difference in tension in 
the steel, measured in pounds. It is the amount of tension which 
must be transferred to the concrete in that unit-length of the beam. 
But the computation of the difference of moments at two sections 
that are only a unit-distance apart, is a comparatively tedious opera- 
tion, which, fortunately, is unnecessary. Theoretical mechanics 
teaches us that the difference in the moment at two consecutive 
sections of the beam is measured by the total vertical shear in the 
beam at that point. The shear is very easily and readily computable; 
and therefore the required amount of tension to be transferred from 
the steel to the concrete can readily be computed. A numerical illus- 
tration may be given as follows : Suppose that we have a beam which, 
with its load, weighs 20,000 pounds, on a span of 20 feet. Using 
ultimate values, for which we multiply the loading by 4, we have an 
ultimate loading of 80,000 pounds. Therefore, 

y o ."j^i. 80,000 IX 240 =2)400000 

o o 

Using the constants previously chosen for 1:3:5 concrete, and there- 
fore utilizing Equation 23, we have this moment equal to 397 b d 2 . 
Therefore b d 2 = 6,045. 

If we assume b = 15 inches; d = 20.1 inches; then d — x = 
.&6d = 17.3 inches. The area of steel equals: 

A = .0084 b d = 2.53 square inches. 
We know from the laws of mechanics, that the moment diagram for 
a beam which is uniformly loaded is a parabola, and that the ordinate 



204 MASONRY AXD REINFORCED CONCRETE 

to this curve at a point one inch from the abutment will, in the above 
case, equal (-H~g-) 2 of the ordinate at the abutment. This ordinate 
is measured by the maximum moment at the center, multiplied by 

the factor (yio ) 2 = ' = .9834 ; therefore the actual moment 

at a point one inch from the abutment = (1.00 — .9834) = .0166 of 
the moment at the center. But .0166 X 2,400,000 = 39,840. 

But our ultimate loading being 80,000 pounds, we know that the 
shear at a point in the middle of this one-inch length equals the shear 
at the abutment, minus the load on this first \ inch, which is ^tw of 
40,000 (or 167) pounds. The shear at this point is therefore 40,000 — 
167 (or 39,833) pounds. This agrees with the above value 39,840, 
as closely as the decimals used in our calculations will permit. 

The value of d — x is somewhat larger when the moment is very 
small than when it is at its ultimate value. But the difference is 
comparatively small, is on the safe side, and it need not make any 
material difference in our calculations. Therefore, dividing 39,840 
by 17.3, we have 2,303 pounds as the difference in tension in the steel 
in the last inch at the abutment. Of course this does not literally 
mean the last inch in the length of the beam, since, if the net span 
were 20 feet, the actual length of the beam would be considerably 
greater. The area of the steel as computed above is 2.53 square 
inches. Assuming that this is furnished by five f-inch square bars, 
the surfaces of these five bars per inch of length equals 15 square 
inches. Dividing 2,303 by 15, we have 153 pounds per square inch 
as the required adhesion between the steel and the concrete. While 
this is not greater than the adhesion usually found between concrete 
and steel, it is somewhat risky to depend on this; and therefore the 
bars are usually bent so that they run diagonally upward, and thus 
furnish a very great increase in the strength of the beam, which pre- 
vents the beam from failing at the ends. Tests have shown that 
beams which are reinforced by bars only running through the lower 
part of the beam without being turned up, or without using any 
stirrups, will usually fail at the ends, long before the transverse 
moment, which they possess at their center, has been fully developed. 

278. Distribution of Vertical Shears. Beams which are tested 
to destruction frequently fail at the ends of the beams, long before 
the transverse strength at the center has been fully developed. Even 



MASONRY AND REINFORCED CONCRETE 



205 




if the bond between the steel and the concrete is amply strong for the 
requirements^ the beam may fail on account of the shearing or diag- 
onal stresses in the concrete between the steel and the neutral axis. 
The student must accept without proof some of the following state- 
ments regarding the distribution of the shear. 

The intensity of the shear of various points in the height of the 
beam, may be represented by the diagram in Fig. 99. If we ignore 
the tension in the concrete due to transverse bending, the shear will 
be uniform between the steel and the neutral 
axis. Above the neutral axis, the shear will 
diminish toward the top of the beam, the 
curve being parabolic. 

If the distribution of the shear were ~~ 
uniform throughout the section, we might 
say that the shear per square inch would 
equal V -f- b do It may be proved that v, 
the intensity of the vertical shear per square 
inch, is: 

b (d — x) 

In the above case, the ultimate total shear V in the last inch at 

the end of the beam, is 39,840 pounds. Then, 

39,840 lco _ , . , 

v = \y 17Q = 153.5 pounds per square men, 
lo X 17.3 

The agreement of this numerical value of the unit-intensity of the 
vertical shear with the required bond between the concrete and the 
steel, is due to the accidental agreement of the width of the beam 
(15 inches) with the superficial area of the bars per inch of length of 
the beam (15 square inches). If other bars of the same cross-sec- 
tional area, but with greater or less superficial surface, had been 
selected for the reinforcement, even this accidental agreement would 
not have been found. 

The actual strength of concrete in shear is usually far greater 
than this. The failure of beams which fail at the ends when loaded 
with loads far within their capacity for transverse strength, is gener- 
ally due to the secondary stresses. The computation of these stresses 
is a complicated problem in Mechanics; but it may be proved that if 
we ignore the tension in the concrete due to bending stresses, the 



Fig. 99. Intensity of Shear at 

Various Points in Height 

of Beam. 



206 MASONRY AND REINFORCED CONCRETE 

diagonal tension per unit of area equals the vertical shear per unit of 
area (v). But concrete which may stand a shearing stress of 1,000 
pounds per square inch will probably fail under a direct tension of 
200 pounds per square inch. The diagonal stress has the nature of a 
direct tension. In the above case the beam probably would not fail 
by this method of failure, since concrete can usually stand a tension 
up to 200 pounds per square inch; but such beams, when they are 
not diagonally reinforced, frequently fail in that way before their 
ultimate loads are reached. 

279. Methods of Guarding against Failure by Shear or Diagonal 
Tension. The failure of a beam by actual shear is almost unknown. 
The failures usually ascribed to shear are generally caused by diagonal 
tension. A solution of the very simple Equation 31 will indicate 
the intensity of the vertical shear. 

The relation of crushing strength to shearing strength is ex- 
pressed by the equation : 

Unit shearing strength z 



2 tan ' 

in which z is the unit shearing strength, and 6 is the angle of rupture 
under direct compression. This angle is usually considered to be 
60°; for such a value the shearing strength would equal c'-f- 3.464. 
When 6 = 45°, the shearing strength would equal one-half of the 
crushing strength, and this agrees very closely with the results of 
tests made by Professor Spofford. But the shearing strength is con- 
sidered to be a far less reliable quantity than the crushing strength; 
and therefore dependence is not placed on shear, even for ultimate 
loading, to a greater value than about one-half of the above value; or, 

Unit shearing strength z = c' -f- 6.928. 

Usually the unit-intensity of the vertical shear (even for ultimate 
loads) is less than this. But this ignores the assistance furnished by 
the bars. Actual failure would require that the bars must crush the 
concrete under them. When, as is usual, there are bars passing 
obliquely through the section, a considerable portion of the shear is 
carried by direct tension in the bars. 

It seems impracticable to develop a rational formula for the 
amount of assistance furnished by these diagonal bars, unless we 
make assumptions which are doubtful and which therefore vitiate 



MASONRY AND REINFORCED CONCRETE 207 

the reliability of the whole calculation. Therefore the rules which 
have been suggested for a prevention of this form of failure are wholly 
empirical. Mr. E. L. Ransome uses a rule for spacing vertical 
stirrups, made of wires or f-inch rods, as follows : 

The first stirrup is placed at a distance from the end of the beam 
equal to one-fourth the depth of the beam; the second is at a distance 
of one-half the depth beyond the first stirrup; the third, three-fourths 
of the depth beyond the second ; and the fourth, a distance equal to 
the depth of the beam beyond the third (see Fig. 100). This empir- 
ical rule agrees with the theory, in the respect that the stirrups are 



'/* 



m — 1 ~wm 



*%&. 



mZti 



\ ' \ ! ! I 



Fig. 100. Spacing of Stirrups. 



closer at the ends of the beam, where the shear is greatest. The four 
stirrups extend for a distance from the end equal to 2h times the depth 
of the beam. Usually this is a sufficient distance; but some "sys- 
tems" use stirrups throughout the length of the beam. On very short 
beams, the shear changes so rapidly that at 2\ times the depth from 
the end of the beam the shear is not generally so great as to produce 
dangerous stresses. With a very long beam, the change in the 
shear is correspondingly more gradual; and it is possible that stir- 
rups or some other device must be used for a greater actual distance 
from the end, although for a less proportional distance. 

When the diagonal reinforcement is accomplished by bending 
up the bars at an angle of about 45°, the bending should be done so 
that there is at all sections a sufficient area of steel in the lower part 
of the beam to withstand the transverse moment at that section. As 
fast as the bars can be spared from the bottom of the beam, they 
may be turned up diagonally so that there are at every section of the 
beam one or more bars which would be cut diagonally by such a 
section. On this account it is far better to use a larger number of 
bars, than a smaller number of the same area. For example, if it 
were required that there shall be 2.25 square inches of steel for the 
section at the middle of the beam, it would be far better to use nine 
2-inch bars than four f-inch bars. In either case, the steel has the 



208 MASONRY AND REINFORCED CONCRETE 

same area and the same weight. The nine |-inch bars give a much 
better distribution of the metal. The superficial area of the nine 
J-inch bars is 18 square inches per linear inch of the beam, while the 
area of the four f-inch bars is only 12 square inches per inch of length. 
But an even greater advantage is furnished by the fact that we have 
nine bars instead of four, which may be bent upward (and bent more 
easily than the f-inch bars) as fast as they can be spared from the 
bottom of the beam. In this way the shear near the end of the beam 
may be much more effectually and easily provided for. 

Since the shear is greatest at the ends of the beam, more bars 
should be reserved for turning up near the ends. For example, in the 
above case of the nine bars, one or two bars might be turned up at 
about the quarter-points of the beam. One or two more might be 
turned up at a distance equal to, or a little less than, the depth of the 
beam from the quarter-points toward the abutments. Others would 
be turned up at intermediate points; at the abutments there should 
be at least two, or perhaps three, diagonal bars, to take up the maxi- 
mum shear near the abutments. This is illustrated, although with- 
out definite calculations, in Fig. 101. 




V' 2 bars X %_ _ JS \_. 




Fig. 101. Bars Turned Up to Take Up Shear near Ends of Beam. 

280. Detailed Design of a Plain Beam. This will be illustrated 
by a numerical example. A beam having a span of 18 feet supports 
one side of a 6-inch slab 8 feet wide which carries a live load of 200 
pounds per square foot. In addition, a special piece of machinery, 
weighing 2,400 pounds, is located on the slab so near the middle of 
the beam that we shall consider it to be a concentrated load at the 
center of the beam. The floor area carried by the beam is 18 feet by 
4 feet = 72 square feet. Adding 3 inches to the 6 inches thickness 
of the slab as an allowance for the weight of the beam, we have 
9 X 12 = 108 pounds per square foot for the dead weight of the floor. 
With a factor of 2 for dead load, this equals 216. Using a factor of 
4 on the live load (200), we have 800 pounds per square foot. Then 
the ultimate load on the beam, due to these sources, is (216 + 800) 



MASONRY AND REINFORCED CONCRETE 209 

72 = 73,152 pounds. So far as its effect on moment is concerned, 
the concentrated load of 2,400 pounds at the center would have the 
same effect as 4,800 pounds uniformly distributed. As it is a piece of 
vibrating machinery, we shall use a factor of six (6), and thus have 
an ultimate effect of 6 X 4,800 = 28,800 pounds. Adding this to 
73,152, we have 101,952 pounds as the equivalent, ultimate, uniformly 
distributed load. Then, 

M = i Wo I =1 X 101,952 X 216 = 2,752,704. 



2400 lbs. 

is'-cr 

CD ' 



^mz soo Ibs.pe-r. sq.ft. 

f ™\__i_J i i * ♦ ♦ i i I II i i i ; i I 4 i ij_j 




iiiiii 



< 



-.K-e^^T 



7 I'll 'I »• 

6-§sq;.bars \~ i2 "4 * Section A B 

Fig. 102. Reinforced Beam. 

In order to reduce as much as possible the size and weight of this 
beam, we shall use 1:2:4 concrete, and therefore apply Equation 24: 

2,752,704 = 565 bd 2 ; 
bd 2 = 4,872. 

If b =16 inches, d 2 = 304.5, and d = 17.5 inches. 

A still better combination would be a deeper and narrower beam 
with b = 12 inches, and d = 20.15 inches. With this combination, 
the required area of the steel will equal : 

A = .0121 X bd = .0121 X 12 X 20.15 = 2.93 square inches. 

This can be supplied by eight bars f inch square. 

The total ultimate load as determined above, is 101,952 pounds. 
One-half of this gives the maximum shear at the ends, or 50,976 
pounds. Applying Equation 31, we have, since d — x = .85 d = 17 
inches : 

V 50,796 j . , 

v = 1 -— -^ r = — - 1 — — = 249 pounds per square men. 

b (d-x) 12 X 17 F ^ h 

As already discussed in previous cases, the ends of the beam must 
be reinforced against diagonal tension, since the above value of v is 
too great, even as an ultimate value, for such stress. Therefore the 



210 MASONRY AND REINFORCED CONCRETE 



ends of the beam must be reinforced by turning the bars up, or by the 
use of stirrups. The beam must therefore be reinforced about as 
shown in Fig. 102. Although the concentrated center load in this 
case is comparatively too small to require any change in the design, it 
should not be forgotten that a concentrated load may cause the shear 
to change so rapidly that it might require special provision for it by 
means of stirrups in the center of the beam, where there is ordinarily 
no reinforcement which will assist shearing stresses. 

281. Effect of Quality of Steel. There is one very radical dif- 
ference between the behavior of a concrete-steel structure and that of 
a structure composed entirely of steel, such as a truss bridge. A truss 
bridge may be overloaded with a load which momentarily passes the 
elastic limit, and yet the bridge will not necessarily fail, nor cause the 
truss to be so injured that it is useless and must be immediately 
replaced. The truss might sag a little, but no immediate failure is 
imminent. On this account, the factor of safety on truss bridges is 
usually computed on the basis of the ultimate strength. 

A concrete-steel structure acts very differently. As has already 
been explained, the intimate union of the concrete and the steel at 
all points along the length of the bar (and not merely at the ends), 
is an absolute essential for stability. If the elastic limit of the steel 
has been exceeded owing to an overload, then the union between the 
concrete and the steel has unquestionably been destroyed, provided 
that union depends on mere adhesion. Even if that union is assisted 
by a mechanical bond, the distortion of the steel has broken that bond 
to some extent, although it will still require a very considerable force 
to pull the bar through the concrete. It is therefore necessary that 
the elastic limit of the steel should be considered the virtual ultimate 
so far as the strength of the steel is concerned. It is accordingly con- 
sidered advisable, as already explained, to multiply all working loads 
by the desired factor of safety (usually taken as 4), and then to pro- 
portion the steel and concrete so that such an ultimate load will 
produce crushing in the upper fibre of the concrete, and at the same 
time will stress the steel to its elastic limit. On this basis, economy 
in the use of steel requires that the elastic limit should be made 
as high as possible. 

The manufacture of steel of very high elastic limit requires the 
use of a comparatively large proportion of carbon, which may make 



MASONRY AND REINFORCED CONCRETE 211 

the steel objectionably brittle. The steel for this purpose must 
therefore avoid the two extremes — on the one hand, of being brittle; 
and on the other, of being so soft that its elastic limit is very low. 

Several years ago, bridge engineers thought that a great economy 
in bridge construction was possible by using very high carbon steel, 
which has not only a high elastic limit but also a correspondingly high 
ultimate tensile strength. But the construction of such bridges 
requires that the material shall be punched, forged, and otherwise 
handled in a way that will very severely test its strength and perhaps 
cause failure on account of its brittleness. The stresses in a concrete- 
steel structure are very different. The steel is never punched; the 
individual bars are never subjected to transverse bending after being 
placed in the concrete. The direct shearing stresses are insignificant. 
The main use, and almost the only use, of the steel, is to withstand a 
direct tension; and on this account a considerably harder steel may 
be used than is usually considered advisable for steel trusses. 

If the structure is to be subject to excessive impact, a somewhat 
softer steel will be advisable; but even in such a case, it should be 
remembered that the mere weight of the structure will make the 
effect of the shock far less than it would be on a skeleton structure of 
plain steel. The steel ordinarily used in bridge work, generally has an 
elastic limit of from 30,000 to 35,000. If we use even 33,000 pounds 
as the value for s on the basis of ultimate loading, we shall find that 
the required percentage of steel is very high. On the other hand, 
if we use a grade of steel in which the carbon is somewhat higher, 
having an ultimate strength of about 90,000 to 100,000 pounds per 
square inch, and an elastic limit of 55,000 pounds per square inch, 
the required percentage of steel is much lower. 

282. Slabs on I=Beams. There are still many engineers who 
will not adopt reinforced concrete for the skeleton structure of build- 
ings, but who construct the frames of their buildings of steel, using 
steel I-beams for floor-girders and beams, and then connect the beams 
with concrete floor-slabs (Fig. 103). These are usually computed on 
the basis of transverse beams which are free at the ends, instead of 
considering them as continuous beams, which will add about 50 per cent 
to their strength. Since it would be necessary to move the reinforcing 
steel from the lower part to the upper part of the slab when passing 
over the floor-beams, in order to develop the additional strength which 



212 



MASONRY AND REINFORCED CONCRETE 



is theoretically possible with continuous beams, and since this is not 
usually done, it is by far the safest practice to consider all floor-slabs as 
being "free-ended." The additional strength which they un- 
doubtedly have to some extent because they are continuous over the 
beams, merely adds indefinitely to the factor of safety. Usually the 
requirement that the I-beams shall be fireproof ed by surrounding the 
beam itself with a layer of concrete such that the outer surface is at 
least 2 inches from the nearest point of the steel beam, results in 








Longitudinal ibdrs to prevent 
shrink cage croicks. 
Expanded. Tnetdl 
or- wire Icath. 



Fig. 103. Concrete Floor-Slabs on I-Beam Girders. 

having a shoulder of concrete under the end of each slab, which quite 
materially adds to its structural strength. But usually no allowance 
is made; nor is there any reduction in the thickness of the. slab on 
account of this added strength. In this case also, the factor of safety 
is again indefinitely increased. The fireproofing around the beam 
must usually be kept in place by wrapping a small sheet of expanded 
metal or wire lath around the lower part of the beam before the con- 
crete is placed. 

Slabs Reinforced in Both Directions. When the floor-beams 
of a floor are spaced nearly equally in both directions, so as to 
form, between the beams, panels which are nearly square, a material 
saving can be made in the thickness of the slab by reinforcing it with 
bars running in both directions. The theoretical computation of the 
strength of such slabs is exceedingly complicated. It is usually con- 
sidered that such slabs have twice the strength of a slab supported 
only on two sides and reinforced with bars in but one direction. The 
usual method of computing such slabs is to compute the slab thick- 
ness, and the spacing and size of the reinforcing steel, for a slab which 
is to carry one-half of the actual load. Strictly speaking, the slab 
should be thicker by the thickness of one set of reinforcing bars. 

283. Reinforcement against Temperature Cracks. The modulus 
of elasticity of ordinary concrete is approximately 2,400,000 pounds 



MASONRY AND REINFORCED CONCRETE 213 

per square inch, while its ultimate tensional strength is about 200 
pounds per square inch. Therefore a pull of about Y2~hyww °f the 
length would nearly, if not quite, rupture the concrete. The coefficient 
of expansion of concrete has been found to be almost identical with 
that of steel, or .0000065 for each degree Fahrenheit. Therefore, if a 
block of concrete were held at the ends with absolute rigidity, while 
its temperature were lowered about 12 degrees, the stress developed 
in the concrete would be very nearly, if not quite, at the rupture point. 
Fortunately the ends will not usually be held with such rigidity; but 
nevertheless it does generally happen that, unless the entire mass of 
concrete is permitted to expand and contract freely so that the tem- 
perature stresses are small, the stresses will usually localize themselves 
at the weak point of the cross-section, wherever it may be, and will 
there develop a crack, provided the concrete is not reinforced with 
steel. If, however, steel is well distributed throughout the cross- 
section of the concrete, it will prevent the concentration of the stresses 
at local points, and will distribute it uniformly throughout the mass. 

Reinforced-concrete structures are usually provided with bars 
running in all directions, so that temperature cracks are prevented 
by the presence of such bars, and it is generally unnecessary to make 
any special provision against such cracks. The most common ex- 
ception to this statement occurs in floor-slabs, which structurally 
require bars in only one direction. It is found that cracks parallel 
with the bars which reinforce the slab will be prevented if a few bars 
are laid perpendicularly to the direction of the main reinforcing bars. 
Usually J-inch or f-inch bars, spaced about 2 feet apart, will be 
sufficient to prevent such cracks. 

Retaining walls, the balustrades of bridges, and other similar 
structures, which may not need any bars for purely structural reasons, 
should be provided with such bars in order to prevent temperature 
cracks. A theoretical determination of the amount of such rein- 
forcing steel is practically impossible, since it depends on assumptions 
which are themselves very doubtful. It is usually conceded that if 
there is placed in the concrete an amount of steel whose cross-sectional 
area equals about J of 1 per cent of the area of the concrete, the 
structure will be proof against such cracks. Fortunately, this amount 
of steel is so small that any great refinement in its determination is of 
little importance. Also, since such bars have a value in tying the 



214 



MASONRY AND REINFORCED CONCRETE 



structure together, and thus adding somewhat to its strength and 
ability to resist disintegration owing to vibrations, the bars are 
usually worth what they cost. 

STRENGTH OF T=BEAMS 



284. When concrete beams are laid in conjunction with over- 
lying floor-slabs, the concrete for both the beams and the slabs being 
laid in one operation, the strength of such beams is very much greater 
than their strength considered merely as, plain beams, even though we 
compute the depth of the beams to be equal to the total depth from 
the bottom of the beam to the top of the slab. An explanation of this 
added strength may be made as follows: 

If we were to construct a very wide beam with a cross-section 
such as is illustrated in Fig. 104, there is no hesitation about calcu- 
lating such strength as that of a plain beam whose width is b } and 

whose effective depth to the rein- 
forcement is d. Our previous study 
in plain beams has shown us that the 
steel in the bottom of the beam takes 
care of practically all the tension; 
that the neutral axis of the beam is 
somewhat above the center of its 
height; that the only work of the 
concrete below the neutral axis is to 
transfer the stress in the steel to the 
Fig. 104. T-Beam in Cross-Section. concrete in the top of the beam ; and 
that even in this work it must be assisted somewhat by stirrups or by 
bending up the steel bars. If, therefore, we cut out from the lower cor- 
ners of the beam two rectangles, as shown by the unshaded areas, we 
are saving a very large part of the concrete, with very little loss in the 
strength of the beam, provided we can fulfil certain conditions. The 
steel, instead of being distributed uniformly throughout the bottom of 
the wide beam, is concentrated into the comparatively narrow portion 
which we shall hereafter call the rib of the beam. The concentrated 
tension in the bottom of this rib must be transferred to the compres- 
sion area at the top of the beam. We must also design the beam so 
that the shearing stresses in the plane (mri) immediately below the 




MASONRY AND REINFORCED CONCRETE 



215 



slab shall not exceed the allowable shearing stress in the concrete. 
We must also provide that failure shall not occur on account of shear- 
ing in the vertical planes (m r and n s) between the sides of the beam 
and the flanges. 

285. Resisting Moments of T=Beams. These will be com- 
puted in accordance with straight-line formulae. There are three 
possible cases, according as the neutral axis is: (1) below the bottom 
of the slab (which is the most common case, and which is illustrated 
in Fig. 105); (2) at the bottom of the slab; or (3) above it. All pos- 
sible effect of tension in the concrete is ignored. For Case 1, even the 
compression furnished by the concrete between the neutral axis and 
the under side of the slab is ignored. Such compression is of course 



tsg^lNeutrttl Ax is 

mr 



I 



2 



W 



it 



2 



I 



Fig. 105. Compression Stress Diagram for T-Beam. 



zero at the neutral axis; its maximum value at the bottom of the 
slab is small; the summation of the compression is evidently small; 
the lever arm is certainly not more than f z/; therefore the moment 
due to such compression is insignificant compared with the resisting 
moment due to the slab. The computations are much more com- 
plicated; the resulting error is a very small percentage of the true 
figure, and the error is on the side of safety. 

286 Case 1 . If c is the maximum compression at the top of the 
slab, and the stress-strain diagram is rectilinear, as in Fig. 105, then 

the compression at the bottom of the slab is c ? ^ . The average 

kd-t 

compression 



kd 



= h{c + c 



kd 



) = — (kd - £ t). The total corn- 
ea 



pression equals the average compression multiplied by the area b't; or, 
C = As= b't JL-(jcd—}t) (32) 



216 MASONRY AND REINFORCED CONCRETE 



The center of gravity of the compressive stresses is evidently at the 
center of gravity of the trapezoid of pressures. The distance x of 
this center of gravity from the top of the beam is given by the formula : 

(M) 



_ t 3 kd - 2 t 
* ~3 2 kd-t 



It has already been shown in Article 264, that : 

e c cr kd 

e s s d — kd 

Combining this equation with Equation 32, we may eliminate — , 



and obtain a value for kd : 



Ard.+ lb't* (34) 

Ar + b't ' 



If the percentage of steel is chosen at random, the beam will probably 
be over-reinforced or under-reinforced. In general it will therefore 
be necessary to compute the moment with reference to the steel and 
also with reference to the concrete, and, as before with plain beams 
(Equation 29), we shall have a pair of equations : 

M c = C (d-x) = Vt~ (kd - \ (d - x) j /3 5 \ 

M s = As (d-x) = pb'ds {d-x) 

287. Case 2. If we place kd = t in the equation above 
Equation 34, and solve for d, we have a relation between d, c, s, r, and 
t, which holds when the- neutral axis is just at the bottom of the slab. 
The equation becomes : 

d ^ cr + *) (36) 

cr 

A combination of dimensions and stresses which would place the 
neutral axis exactly in this position, is improbable, although readily 
possible; but Equation 36 is very useful to determine whether a given 
numerical problem belongs to Case 1 or Case 3. When the stresses s 
and c in the steel and concrete, the ratio r of the elasticities, and the 
thickness t of the slab are all determined, then the solution of Equa- 
tion 36 will give a value of d which would bring the neutral axis at the 
bottom of the slab. But it should not be forgotten that the com-, 
pression in the concrete (c) and the tension in the steel will not 
simultaneously have certain definite values (say c = 500, and .9 = 
16,000) unless the percentage of steel has been so chosen as to give 



MASONRY AND REINFORCED CONCRETE 217 

those simultaneous values. When, as is usual, some other percentage 
of steel is used, the equation is not strictly applicable, and it therefore 
should not be used to determine a value of d which will place the 
neutral axis at the bottom of the slab and thus simplify somewhat the 
numerical calculations. For example, for c = 500, s = 16,000, 
r = 12, and t = 4 inches, d will equal 14.67 inches. Of course this 
particular depth may not satisfy the requirements of the problem. 
If the proper value for d is less than that indicated by Equation 36, 
the problem belongs to Case 3; if it is more, the problem belongs to 
Case 1. 

288. Case 3. The diagram of pressure is very similar to that in 
Fig. 105, except that it is a triangle instead of a trapezoid, the triangle 
having a base c and a height kd which is less than t. The center of 
compression is at J the height from the base, or x = J kd. Equa- 
tions 25 to 29 are applicable to this case as well as to Case 2, which 
may be considered merely as the limiting case to Case 3. But it 
shoulpl be remembered that V refers to the width of the flange or 
slab, and not to the width of the stem or rib. 

289. Width of Flange. The width (6') of the flange is usually 
considered to be equal to the width between adjacent beams, or that 
it extends from the middle of one panel to the middle of the next. 
The chief danger in such an assumption lies in the fact that if the 
beams are very far apart, they must have corresponding strength 
to carry such a floor load, and the shearing stresses between the rib 
and the slab will be very great. The method of calculating such 
shear will be given later. It sometimes happens (as illustrated in 
Article 296), that the width of slab on each side of the rib is almost 
indefinite. In such a case we must arbitrarily assume some limit, 
and say that the compression in the slab which is due to the T- 
beam is confined to a strip which is (say) fifteen or twenty times the 
thickness of the slab. If the compression is computed for two cases, 
both of which have the same size of rib, same steel, same thickness of 
slab, but different slab widths, it is found, as might be expected, that 
for the narrower slab width the unit-compression is greater, the 
neutral axis is very slightly lower, and even the unit-tension in the 
steel is slightly greater. No demonstration has ever been made to 
determine any limitation of width of slab beyond which no com- 
pression would be developed by the transverse stress in a T-beam 



218 MASONRY AND REINFORCED CONCRETE 

rib under it. It is probably safe to assume that it extends for seven 
to ten times the thickness of the slab on each side of the rib. If the 
beam as a whole is safe on this basis, then it is still safer for any addi- 
tional width to which the compression may extend. 

290. Width of Rib. Since it is assumed that all of the com- 
pression occurs in the slab, the only work done by the concrete in the 
rib is to transfer the tension in the steel to the slab, to resist the 
shearing and web stresses, and to keep the bars in their proper 
place. The width of the rib is somewhat determined by the amount 
of reinforcing steel which must be placed in the rib, and whether it 
is desirable to use two or more rows of bars instead of merely one row. 
As indicated in Fig. 104, the amount of steel required in the base of 
a T-beam is frequently so great that two rows of bars are necessary 
in order that the bars may have a sufficient spacing between them so 
that the concrete will not split apart between the bars. Although 
it would be difficult to develop any rule for the proper spacing between 
bars without making assumptions which are perhaps doubtful, the 
following empirical rule is frequently adopted by designers: The 
spacing between bars, center to center, should be two and a-quarter times 
the diameter of the bars. Fire insurance and municipal specifications 
usually require that there shall be two inches clear outside of the steel „ 
This means that the beam shall be four inches wider than the net 
width from out to out of the extreme bars. The data given in Table 
XVIII will therefore be found very convenient, since, when it is 
desired to use a certain number of bars of given size, a glance at the 
table will show immediately whether it is possible to space them in 
one row; and, if this is not possible, the necessary arrangement can 
be very readily designed. For example, assume that six f-inch bars 
are to be used in a beam. The table shows immediately that the re- 
quired width of the beam (following the rule) will be 14.72 inches; 
but if, for any reason, a beam 11 inches wide is considered preferable, 
the table shows that four J- inch bars may be placed side by side, 
leaving two bars to be placed in an upper row. Following the same 
rule regarding the spacing of the bars in vertical rows, the distance 
from center to center of the two rows should be 2.25 X .875 = 1.97 
inches, showing that the rows should be, say, two inches apart center 
to center. It should also be noted that the plane of the center of 
gravity of this steel is at two-fifths of the distance between the bars 



MASONRY AND REINFORCED CONCRETE 



219 



TABLE XVIII 

Required Width of Beam, Allowing 2,\£ X cf, for Spacing Center to 
Center, and 2 Inches Clear on Each Side 

Formula: Width = (rc-l)2.25d + d + 4 = 2.25 nd - 1.25 d + 4 



No. of Bars 


i-lN. 


§-In. 


f-lN. 


I-lN. 


1-In. 


U-In. 


2 


5.62 In. 


6.03 In. 


6.44 In. 


6.84 In. 


7.25 In. 


8.06 In. 


3 


6.75 " 


7.44 " 


8.13 " 


8.81 " 


9.50 " 


10.87 " 


4 


7.87 " 


8.84 " 


9.81 " 


10.78 " 


11.75 " 


13.68 " 


5 


9.00 " 


10.25 " 


11.50 " 


12.75 " 


14.00 " 


16.50 " 


6 


10.12 " 


11.65 " 


13.19 " 


14.72 " 


16.25 " 


19.31 " 


7 


11.25 " 


13.06 " 


14.87 " 


16.68 " 


18.50 ■'■' 


22.12 " 


8 


12.37 " 


14.46 " 


16.56 " 


18.65 " 


20.75 " 


24.94 " 


9 


13.50 " 


15.87 " 


18.25 " 


20.62 " 


23.00 " 


27.75 " 


10 


14.62 " 


17.28 " 


19.94 " 


^22. 59 " 


25.25 " 


30.56 '*. 



above the lower row, or that it is eight-tenths of an inch above the 
center of the lower row. 

291. Numerical Illustrations of T=Beams. Example I. Assume that 
a 5-inch slab is supporting a load on beams spaced 8 feet apart, the beams hav- 
ing a span of 20 feet. Assume that the moment of the beam has been computed 
as 900,000 inch-pounds. What will be the dimensions of the beam if the con- 
crete is not to have a compression greater than 500 pounds per square inch and 
the tension of the steel is not to be greater than 16,000 pounds per square 
inch? 

Answer. There are an indefinite number of solutions to this 

problem. There are several terms in Equation 35 which are mutually 

dependent; it is therefore impracticable to obtain directly the depth 

of the beam on the basis of assuming the other quantities; therefore 

it is only possible to assume figures which experience shows will give 

approximately accurate results, and then test these figures to see 

whether all the conditions are satisfied. Within limitations, we may 

assume the amount of steel to be used, and. determine the depth of 

beam which will satisfy the other conditions together with that of the 

assumed area of steel. For example, we shall assume that six f-inch 

square bars having an area of 4.59 square inches will be a suitable 

reinforcement for this beam. We shall also assume as a trial figure 

that x = 1.5. Substituting these values in the second formula of 

Equation 35, we may write the second formula : 

900,000 = 4.59 X 16,000 (d- 1.5). 



220 MASONRY AND REINFORCED CONCRETE 

Solving for d, we find that d = 13.75. If we test this value by 
means of Equation 36, we shall find that, substituting the values of 
t, c, r, and s in Equation 36, the resulting value of d equals 18.33. 
This shows that if we make the depth of the beam only 13.75, the 
neutral axis will probably be within the slab, and the problem comes 
under Case 3, to which we must apply Equation 29. Dividing the 
area of the steel, 4.50, by (&' X d), we have the value of p equals 
.00348. Interpolating with this value of p in Table XV, we find that 
whenr = 12, k = 2.50; Jed = 3.44; x = 1.15; and d - x = 12.6. 
Substituting these values in Equation 29, we find that the moment 
900,000 = 2,082c, or that c = 432 pounds per square inch. This 
shows that the unit-compression of the concrete is safely within 
the required figure. Substituting the known values in the second 
part of Equation 29, we find that the stress in the steel s equals about 
15,500 pounds per square inch. 

Example 2. Assume that a floor is loaded so that the total 
weight of live and dead load is 200 pounds per square foot; assume 
that the T-beams are to be 5 feet apart, and that the slab is to be 4 
inches thick; assume that the span of the T-beams is 30 feet. We 
therefore have an area of 150 square feet to be supported by each 
beam, which will give a total load of 30,000 pounds on each beam. 
The. moment at the center of such a beam will therefore be equal to 
the total load, multiplied by one-eighth of the span (expressed in 
inches), and the moment is therefore 1,350,000 inch-pounds. As a 
trial value, we shall assume that the beam is to be reinforced with 
six f-inch bars, which have an area of 3.37 square inches. Substi- 
tuting this value of the area in the second part of Equation 35, and 
assuming that s = 16,000 pounds per square inch, we find as an 
approximate value for d — x, that it will equal 25 inches. This is 
very much greater than the value of d that would be found from 
substituting the proper values in Equation 36, so that we know at 
once that the problem must be solved by the methods of Case 1. For 
a 4-inch slab, the value of x must be somewhere between 1.33 and 
2.0. As a trial value, we may call it 1.5, and this means that d will 
equal 26.5. Assuming that this slab is to be made of concrete using 
a value for r — 12, we know all the values in Equation 34, and may 
solve for Jed, which we find to equal 5.54 inches. As a check on the 
approximations made above, we may substitute this value of led, and 



MASONRY AND REINFORCED CONCRETE 221 

also the value of t in Equation 33 f and obtain a more precise value 
of x, which we find to equal 1.62. Substituting the value of the 
moment and the other known quantities in the upper formula of 
Equation 35, we may solve for the value of c, and obtain the value 
that c = 352 pounds per square inch. This value for c is so very 
moderate that it would probably be economy to assume a lower 
value for the area of the steel, and increase the unit-compression in 
the concrete; but this solution will not be here worked out*. 

292. Approximate Formulae. A great deal of T-beam com- 
putation is done on the basis that the center of pressure of the con- 
crete is at the middle of the slab, and therefore that the lever-arm of 
the steel = d ■— \ t. From these assumptions we may write the 
approximate formula: 

M s = As(d- l -t) (37) 

If the values of M a and s are known or assumed, we may assume a 
reasonable value for either A or (d — \ t) and calculate the corre- 
sponding value of the other. On the assumption that the slab takes 
all the compression, the distance between the steel and the center of 
compression of the concrete varies between (d — \ t) and (d — .142), 
which is the approximate value when the beam becomes so small that 
it merges into the slab. The smaller value (d — \ t) is the absolute 
limit which is never reached. Therefore the lever-arm is always 
larger than (d — J t). Therefore, if we use Equation 37 to compute 
the area of steel A for a definite moment M s and unit steel tension s, 
the resulting value of A for an assumed depth d, or the resulting 
value of d for an assumed area A, will be larger than necessary. In 
either case the result is safe, but uneconomically so. 

As an illustration, using the values in Example 2, Article 291, of 
M B = 1,350,000; s = 16,000; (d - i t) = (26.5 - 2) - 24.5, the 
resulting value of A = 3 44 square inches, which is larger than the 
more precise value previously computed. 

Equation 37 is particularly applicable when the neutral axis is 
in the rib. Under this condition, the average pressure on the concrete 
of the slab is always greater than J c, or at least it is never less than \c. 
As before explained, the average pressure just equals \c when the 
neutral axis is at the bottom of the slab. We may therefore say that 



222 MASONRY AND REINFORCED CONCRETE 

the total pressure on the slab is always greater than h c b t. We 
therefore write the approximate equation : 

M c =2 cb 'Hd- \t) • • • • (38) 

As before, the values obtained from this equation are safe, but are 
unnecessarily so. Applying them to Example 2, Article 291, by 
substituting M c = 1,350,000, V = 60, t = 4, and (d - \t) = 24.5, 
we compute c = 459. But we know that this approximate value of 
c is greater than the true value ; and if this value is safe, then the true 
value is certainly safe. The more accurate value of c, computed 
in Article 291, is 352. If the value of c in Equation 38 is assumed, 
and the value of d is computed, the result is a depth of beam un- 
necessarily great. 

If the beam is so shallow that we may know, even without the 
test of Equation 36, that the neutral axis is certainly within the slab, 
then we may know that the center of pressure is certainly less than 
J t from the top of the slab, and that the lever-arm is certainly less 
than (d — JO ; and we may therefore modify Equation 37 to read : 

M s = As (d-\t) (39) 

Applying this to ^Example 1 of Article 291, and substituting 
M B = 900,000, s = 16,000, (d - J t) = (13.75 - 1.67) = 12.08, we 
find that A = 4.65, instead of the 4.59 previously computed. This 
again illustrates that the formula gives an excessively safe value, 
although in this case the difference is small. 

Equations 37 and 38 should be considered as a pair which are 
applied according as the steel or the concrete is the determining 
feature. When the percentage of steel is assumed (as is usual), both 
equations should be used to test whether the unit-stresses in both 
the steel and the concrete are safe. It is impracticable to form a 
simple approximate equation corresponding to Equation 39, which 
will express the moment as a function of the compression in the con- 
crete. Fortunately it is unnecessary, since, when the neutral axis 
is within the slab, there is always an abundance of compressive 
strength. 

293. Shearing Stresses between Beam and Slab. Every solu- 
tion for T-beam construction should be tested at least to the extent 



MASONRY AND REINFORCED CONCRETE 



223 



of knowing that there is no danger of failure on account of the shear 
between the beam and the slab, either on the horizontal plane at the 
lower edge of the slab, or in the two vertical planes along the two 
sides of the beam. Let us consider a T-beam such as is illustrated 
in Fig ? 106. In the lower part of the figure is represented one-half of 
the length of the flange, which is considered to have been separated 
from the rib. Following the usual method of considering this as a 




£ 



^ 



L (measured in feet)- 



If 



iillll 



Flange 



1L 



1 



Fig. 106. Analysis of Stresses in T-Beam. 

free body in space, acted on by external forces and by such internal 
forces as are necessary to produce equilibrium, we find that it is acted 
on at the left end by the abutment reaction, which is a vertical force, 
and also by a vertical load on top. We may consider P f to represent 
the summation of all compressive forces acting on the flanges at the 
center of the beam. In order to produce equilibrium, there must be 
a shearing force acting on the under side of the flange. We represent 
this force by S h . Since these two forces are the only horizontal forces, 
or forces with horizontal components, which are acting on this free 
body in space, P f must equal S h . Let us consider z to represent the 
shearing force per unit of area. We know from the laws of me- 
chanics, that, with a uniformly distributed load on the beam, the 
shearing force is maximum at the ends of the beam, and diminishes 
uniformly towards the center, where it is zero. Therefore the average 
value of the unit-shear for the half-length of the beam, must equal 
| z. As before, we represent the width of the rib by b. For conven- 
ience in future computations, we shall consider L to represent the length 
of the beam, measured in feet. All other dimensions are measured in 
inches. Therefore the total shearing force along the lower side of 
the flange, will be: 



-z X b X ^ L X 12 =3bzL 



(40) 



224 MASONRY AND REINFORCED CONCRETE 

There is also a possibility that a beam may fail in case the flange 
(or the slab) is too thin; but the slab is always reinforced by bars 
which are transverse to the beam, and the slab wall be placed on both 
sides of the beam, giving two shearing surfaces. 

294. Numerical Illustration. It is required to test the beam 
which was computed in Example 1 of Article 291. Here the total 
compressive stress in the flange = h cbkd = J X 432 X 96 X 344 
= 71,332 pounds. But this compressive stress measures the shearing 
stress S h between the flange and the rib. 'This beam requires six 
J-inch bars for the reinforcement. We shall assume that the rib is 
to be 11 inches wide, and that four of the bars are placed in the bottom 
row, and two bars about 2 inches above them. The effect of this 
will be to deepen the beam slightly, since d measures the depth of 
the beam to the center of the reinforcement, and, as already computed 
numerically in Article 290, the center of gravity of this combination 
will be T 8 ¥ of an inch above the center of gravity of the lower row of 
bars. Substituting in Equation 40 the values S h = 71,332, b = 11, 
and L = 20, we find, for the unit-value of z, 108 pounds per square 
inch. This shows that the assumed dimensions of the beam are 
satisfactory in this respect, since the true shearing stress permissible 
in concrete is higher than this. 

But the beam must be tested also for its ability to withstand 
shear in vertical planes along the sides of the rib. Since the slab in 
this case is 5 inches thick and we can count on both surfaces to with- 
stand the shear, we have a width of 10 inches to withstand the shear, 
as compared with the 11 inches on the underside of the slab. The 
unit-shear would therefore be ^ of the unit-shear on the under side 
of the slab, and would equal 119 pounds per square inch. Even this 
would not be unsafe, but the danger of failure in this respect is usually 
guarded against by the fact that the slab almost invariably contains 
bars which are inserted to reinforce the slab, and which have such an 
area that they will effectively prevent any shearing in this way. 

Testing Example 2 similarly, we may find the total compression 
C from Equation 32, and that it equals As = 16,000 X 3.37 = 
54,000 pounds. The steel reinforcement is six J-inch bars, and by 
Table XVIII we find that if placed side by side, the beam must be 
13.19 inches in width, or, in round numbers, 13} inches. Substituting 
these values in Equation 37, we find, for the value of z, 45 pounds per 



MASONRY AND REINFORCED CONCRETE 225 

square inch. Such a value is of course perfectly safe. The shear 
along the sides of the beam will be considerably greater, since the 
slab is only four inches thick, and twice the thickness is but 8 inches; 
therefore the maximum unit-shear along the sides will equal 45 
times the ratio of 13.25 to 8, or 75 pounds per square inch. Even 
this would be perfectly safe, to say nothing of the additional shearing 
strength afforded by the slab bars. 

295. Shear in a T=Beam. The shear here referred to is the 
shear of the beam as a whole on any vertical section. It does not 
refer to the shearing stresses between the slab and the rib. 

The theoretical computation of the shear of a T-beam is a 
very complicated problem. Fortunately it is unnecessary to attempt 
to solve it exactly. The shearing resistance is certainly far greater 
in the case of a T-beam than in the case of a plain beam of the same 
width and total depth and loaded with the same total load. There- 
fore, if the shearing strength is sufficient, according to the rule, for 
a plain beam, it is certainly sufficient for the T-beam. In the first 
example of Article 291, the total load on the beam is 30,000 pounds. 
Therefore the maximum shear V at the end of the beam, is 15,000 
pounds. In this particular case, d — x = 12.25. For this beam, d = 
13.75 inches, and 6 = 11 inches. Substituting these values in Equa- 
tion 31, we have: 

V 15,000 rii , . , 

111 pounds per square men. 



b (d-x) 11 X 12.25 

Although this is probably a very safe stress for direct shearing, it is 
more than double the allowable direct tension due to the diagonal 
stresses; and therefore ample reinforcement must be provided. If 
only two of the J-inch bars are turned at an angle of 45° at the end, 
these two bars will have an area of 1.54 square inches, and will have 
a working tensile strength (at the unit-stress of 16,000 pounds) of 
24,640 pounds. This is more than the total vertical shear at the 
ends of the beam; and we may therefore consider that the beam is 
protected against this form of failure. 

296. Numerical Illustration of Slab, Beam, and Girder Con= 
struction. Assume a floor construction as outlined in skeleton form, 
in Fig. 107. The columns are spaced 16 feet by 20 feet. Girders 
which support the alternate rows of beams, connect the columns in 



226 



MASONRY AND REINFORCED CONCRETE 



per 
10, 



girders, 



the 16-foot direction. The live load on the floor is 150 pounc 
square foot. The concrete is to be a 1:2:4 mixture, with r 
and c = 600. Required the proper dimensions for 
beams, and slab. 

The load on the girders may be computed in either one of two 
ways, both of which give the same results. We must consider that 
each beam supports an area of 8 feet by 20 feet. We may therefore 
consider that girder d supports the load of b (on a floor area 8 ft. by 
20 ft.) as a concentrated load in the center. Or, we may consider 

that, ignoring the beams, the 



e 



Kq m 



e 



,Kftm 



e 



team c 



O 



girder supports a uniformly dis- 
tributed load on an area 16 ft. by 
20 ft, The moment in either case 
is the same. Assume that we shall 
use a 1 per cent reinforcement 
in the slab. Then, from Table 
XV, with r = 10, and p = .01, we 
find that k = .358; then x = .119 
d, or (d — x) = .881 d. As a trial, 
we estimate that a 5-inch slab (or d = 4) will carry the load. This 
will weigh 60 pounds per square foot, and make a total live and dead 
load of 210 pounds per square foot. A strip one foot wide and 8 feet 
long will carry a total load of 1,680 pounds, and its moment will be 
J X 1,680 X 96 = 20,160 inch-pounds. Using the first half of 
Equation 29, we can substitute the known values, and say that: 



Fig. 107. Skeleton Outline of Floor-Panel. 



20, 160 = - X 600 X 12 X .358 d X .881 d 

= l,135d 2 
d 2 = 17.76 
d = 4.21 

In this case the span of the slab is considered as the distance from 
center to center of the beams. This is evidently more exact than to 
use the net span (which equals eight feet, less the still unknown width 
of beam), since the true span is the distance between the centers of 
pressure on the two beams. It is probable that the true span (really 
indeterminable) will be somewhat less than 8 feet, which would 
probably justify using the round value of d = 4 inches, and the slab 
thickness as 5 inches, as first assumed. The area of the steel per 



MASONRY AND REINFORCED CONCRETE 22? 



inch of width. of the slab = pbd = .01 X 1 X 4.21 = .0421 square 
inch. Using J-inch round bars whose area equals .1963 square inch, 
the required spacing of the bars will be .1963 -f- .0421 = 4.66 inches. 
Practically this would be called 4f inches. 

The load on a beam is that on an area of 8 feet by 20 feet, and 
equals 8X20X210 = 33,600 pounds for live and dead load. As a 
rough trial value, we shall assume that the beam will be 12 inches 
wide and 15 inches deep below the slab, or a volume of 1 X 1.25 X 20 
cubic feet = 25 cubic feet, which will weigh 3,750 pounds. Adding 
this, we have 37,350 pounds as the total live and dead load carried 
by each beam. The load is uniformly distributed; and the moment: 

M =\ X 37,350 X 240 = 1,120,500 inch-pounds. 

8 

We shall assume that the beam is to have a depth d to the reinforce- 
ment, of 22 inches, and shall utilize Equation 39 to obtain an approxi- 
mate value for the area. Substituting the known quantities in 
Equation 39, we have: 

1,120,500 = A X 16,000 X (22-1.67) 
A = 3.44 square inches. 

For T-beams with very wide slabs and great depth of beam, the 
percentage of steel is always very small. In this case, p = 3.44 -~ 
(96 X 22) = .00163. Such a value is beyond the range of those 
given in Table XV, and therefore we must compute the value of k 
from Equation 27; and we find that k = .165; kd = 3.63, which 
shows that the neutral axis is within the slab; x = \kd = 1.21, and 
therefore (d — x) = 20.79. Substituting these values in the upper 
part of Equation 29 in order to find the value of c, we find that c = 
309 pounds per square inch. Substituting the known values in the 
second half of Equation 29, in order to obtain a more precise value of 
s, we find that s = 15,737 pounds per square inch. 

The required area (3.44 square inches) of the bars will be af- 
forded by six J-inch round bars (6 X .60 = 3.60) with considerable to 
spare. From Table XVIII we find that six J-inch bars (either square 
or round), if placed in one row, would require a beam 14.72 inches 
w T ide. This is undesirably wide, and so we shall use four bars in the 
lower row, and two above, and make the beam 11 inches wide. This 
will add nearly an inch to the depth, and the total depth will be 



228 MASONRY AND REINFORCED CONCRETE 

22 + 3, or 25 inches. The concrete below the slab is therefore 11 
inches wide by 20 inches deep, instead of 12 inches wide by 15 inches 
deep, as assumed when computing the dead load. The section of 
220 square inches will therefore weigh more than the suggested 
section of ISO square inches; but the difference in dead load weight 
is so small that it is unnecessary to alter the calculations, especially 
since the unit-stresses in the concrete and steel are both, lower than 
the working limits. It should also be noted that the span of these 
beams was considered as 20 feet, which is the distance from center to 
center of the columns (or of the girders). This is certainly more 
nearly correct than to use the net span between the columns (or 
girders), which is yet unknown, since neither the columns nor the 
girders are yet designed. There is probably some margin of safety 
in using the span as 20 feet. 

The load on one beam is computed above as 37,350 pounds. 
The load on the girder is therefore the equivalent of this load con- 
centrated at the center, or of double the load (74,700 pounds) uni- 
formly distributed. Assuming for a trial value that the girder will 
be 12 inches by 22 inches below the slab, its weight for sixteen feet 
will be 4,392, or say 4,400 pounds. This gives a total of 79,100 
pounds as the equivalent total live and dead load uniformly dis- 
tributed over the girder. Its moment in the center therefore equals 
i X 79,100 X 192 = 1,898,400 inch-pounds. 

The width of the slab in this case is almost indefinite, being 
twenty feet, or forty-eight times the thickness of the slab. We shall 
therefore assume that the compression is confined to a width of 
fifteen times the slab thickness, or that b' = 75 inches. Assume for 
a trial value that d = 25 inches; then from Equation 39, if s = 
16,000, we find that A = 5.08 square inches. Then p = .0027; and, 
from Equation 27, k = .207, and kd = 5.175. This shows that the 
neutral axis is below the slab, and that it belongs to Case 1, Article 
286. Checking the computation of kd from Equation 34, we com- 
pute kd = 5.18, which is probably the more correct value because 
computed more directly. The discrepancy is due to the dropping 
of decimals during the computations. From Equation 33 f we com- 
pute that x = 1.72; then (d — x) = 23.28. Substituting the 
value of the moment and of the dimensions in the upper part of 
Equation 35, we compute c to be 420 pounds per square inch. Simi- 



MASONRY AND REINFORCED CONCRETE 229 

larly, making substitutions in the lower part of Equation 35, using the 
more precise value of (d — x) for the lever-arm of the steel, we find 
s = 16,052 pounds per square inch. The student should verify 
in detail all these computations. 

The total required area of 5.08 square inches may be divided 
into, say, 8 round bars -J inch in diameter. These would have an area 
of 4.81 square inches. The discrepancy is about five per cent. 
These bars, placed in two rows, would require that the beam should 
be at least 10.78 inches wide. We shall call it 11 inches. The total 
depth of the beam will be three inches greater than d, or 28 inches. 
This means 23 inches below the slab, and the area of concrete below 
the slab is therefore 11 X 23 = 253 square inches, rather than 
12 X 22 = 264 square inches, as assumed for trial. 

Shear. The shearing stresses between the rib and slab of the 
girder are of special importance in this case. The quantity S h of 
Article 293 equals the total compression in the concrete, which equals 
the total tension in the steel, which equals, in this case, 16,052 X 5.08 
= 81,544 pounds. This equals 3 bzl, in which b = 11, I = 16 (feet), 
and z is to be determined. 

z = 81,544 -r- (3 X 11 X 16) = 154 pounds per square inch. 

This measures the maximum shearing stress under the slab, and is 
almost safe, even without the assistance furnished by the stirrups and 
the bars, which would come up diagonally through the ends of the 
beam (where this maximum shear occurs) nearly to the top of the 
slab. The vertical planes on each side of the rib have a combined 
width of 10 inches, and therefore the unit-stress is ■£ J- X 154 = 169 
pounds per square inch. This is a case of true shear, and a 1:2:4 
concrete should stand such a stress with a large factor of safety. 
But there are still other shearing stresses in these vertical planes. 
Considering a strip of the slab, say, one foot wide, which is reinforced 
by slab bars that are parallel to the girder, the elasticity of such a 
strip (if disconnected from the girder) would cause it to sag in the 
center. This must be prevented by the shearing strength of the con- 
crete in the vertical plane along each edge of the girder rib. On 
account of the combined shearing stresses along these planes, it is 
usual to specify that when girders are parallel with the slab bars, bars 
shall be placed across the girder and through the top of the slab for 



230 



MASONRY AND REINFORCED CONCRETE 



the special purpose of resisting these shearing stresses. Some of the 
stresses are indefinite, and therefore no precise rules can be computed 
for the amount of the reinforcement. But since the amount required 
is evidently very small, no great percentage of accuracy is important. 
A recent specification on this point required f-inch bars, 5 feet long, 
spaced 12 inches apart. 

The shear of the girder, taken as a whole, should be computed 
as for simple beams, as. already discussed in Article 295; and stirrups 
should be used, as described in Article 279. 

Another special form of shear must be considered in this problem. 
Where the beams enter the girders, there is a tendency for the beams 
to tear their way out through the girder. The total load on the 
girder by the two beams on each side, is of course equal to the total 
load on one beam, and equals 37,350 pounds. Some of the rein- 
forcing bars of the beam will be bent up diagonally so that they enter 

the girder near its 



top, and therefore 
the beam could not 
tear out w i t h o u t 
shearing through 
the girder from near 
its top or for a depth 
of, say, 22 inches (3 
inches less than d). 
We therefore have 2 X 22 X 11 = 484 square inches, the area to be 
sheared out. Dividing this into 37,350 gives 77 pounds per square inch. 
Although this is probably a safe shearing stress, many engineers would 
consider it advisable to use special V-shaped stirrups (see a, Fig. 108) to 
strengthen the beam against such stress. If the angle of these stirrups 
with the vertical is, say, 45°, then the stress in the bars on each side will 
be .707 of the total load, assuming that these bars were to take all the 
stress. This would mean that these bars would have a stress of about 
26,406 pounds, and at 16,000 pounds per square inch would require a 
total area of 1.65 square inches. Three J-inch bars would therefore 
more than provide the necessary area, even assuming that these stirrups 
took the entire load, and disregarding the stirrups such as would 
ordinarily be placed in the beam, and also disregarding the shearing 
strength of the concrete. If, therefore, these stirrups are made of 




Fig. 108. 



Detail of Reinforcement at Junction of Beam 
and Girder. 



MASONRY AND REINFORCED CONCRETE 



231 



J-inch bars instead of f-inch bars, the shearing stresses in the con- 
crete due to the beam will be amply provided for. A complete de- 
tailed drawing will show all of the bars required for a panel between 
four of these columns. The student should study this drawing (see 
Fig. 109) in connection with the foregoing demonstrations of the 
dimensions of the bars and of the concrete. 

FOOTINGS 
297. Simple Footings. When a definite load, such as a weight 
carried by a column, is to be supported on a subsoil whose bearing 

^ r~-\ 

"s V I L Ail tin 







Cf ^^CTE^^ f] 




3 iarj 4 o 



£ o -spaced f-r 

I I i I I ' ' 



r — t, 



:-H iii iTliiiiilfriM : 



r~g M^^^#^rt#£-Bgii; 



T 1-1 I * I > ' ' 

i ■ i ' 



' i J i J ' i i 



iii:! ijiiil!!:! 






I III 

Lji,.ui;. 

i r i I 

4.+ L.L' I- 

iijii'i 



Mi-, 

li-U 4 4-{-l-' 

1 ! i ' ! ' i 

I ' . I ' I 
1 ' ' ' i ! ! 






II 



1 1 rp 



rl-l-l 



r*Hr 

nh 



iT^Hi 



*rnn 



+ L 






'TJ 



Fig. 109. Detail of Floor-Panel. 



power has been estimated at some definite figure, the required area 
of the footing becomes a perfectly definite quantity, regardless of the 
method of construction of the footing. But with the area of the 
footing once determined, it is possible to effect considerable economy 
in the construction of the footing, by the use of reinforced concrete. 
An ordinary footing of masonry is usually made in a pyramidal form, 
although the sides will be stepped off instead of being made sloping. 
It may be approximately stated that the depth of the footing below 
the base of the column, when ordinary masonry is used, must be 



232 



MASONRY AND REINFORCED CONCRETE 




practically equal to the width of the footing. The offsets in the 
masonry cannot ordinarily be made any greater than the heights of 
the various steps. Such a plan requires an excessive amount of 
masonry. 

A footing of reinforced concrete consists essentially of a slab, 
which is placed no deeper in the ground than is necessary to obtain a 
proper pressure from the subsoil In the simplest case, the column 
is placed in the middle of the footing, and thus acts as a concentrated 
load in the middle of the plate (Fig. 110) . The mechanics of such a 

problem are somewhat simi- 
lar to those of a slab sup- 
ported on four sides and car- 
rying a concentrated load in 
the center, with the very im- 
portant exception, that the 
resistance, instead of being 
applied merely at the edges 
of the slab, is uniformly dis- 
tributed over the entire sur- 
face. Since the column has 
a considerable area, and the 
slab merely overlaps the 
column on all sides, the com- 
mon method is to consider 
the overlapping on each side 
to be an inverted cantilever 
carrying a uniformly distrib- 
uted load, which is in this 
case an upward pressure. 
The maximum moment evidently occurs immediately below each 
vertical face of the column. At the extreme outer edge of the slab 
the moment is evidently zero, arid the thickness of the slab may 
therefore be reduced considerably at the outer edge. The depth of 
the slab, and the amount of reinforcement, which is of course placed 
near the bottom, can be determined according to the usual rules for 
obtaining a moment. This can best be illustrated numerically. 

Example. Assume that a load of 252,000 pounds is to be carried 
by a column, on a soil which consists of hard, firm gravel. Such soil 



TTvH-nH-i-hf-" 

t+rn-rrbft- 1 



4-W-H-H-+-H-- 

7WTT1 i ,Tt"t 



|T1 i 

FPUffl. t 



1 

T 

rr 

rT 

■+ 

-4 
-L 

i 
I 

T 



Fig. 110. Simple Footing of Reinforced Concrete 



MASONRY AND REINFORCED CONCRETE 233 

will ordinarily safely carry a load of 7,000 pounds per square foot. 
On this basis, the area of the footing must be 36 square feet, and 
therefore a footing 6 feet square will answer the purpose. A concrete 
column 24 inches square will safely carry such a loading. Placing 
such a column in the middle of a footing will leave an offset 2 feet 
broad outside each face of the column. We may consider a section 
of the footing made by passing a vertical plane through one face of the 
column. This leaves a block of the footing 6 feet long and 2 feet 
wide, on which there is an upward pressure of 12 X 7,000 = 84,000 
pounds. The center of pressure is 12 inches from the section, and 
the moment is therefore 12 X 84,000 = 1,008,000 inch-pounds. 
Multiplying this by 4, we have 4,032,000 inch-pounds as the ultimate 
moment. Applying Equation 21, we place this equal to 397 bd 2 , in 
which b = 72 inches. Solving this for d, we have d = 11.9 inches. 
A total thickness of 15 inches would therefore answer the purpose. 
The amount of steel required per inch of width = .0084 d = .0084 
X 11.9 = .100 square inch of steel per inch of width. Therefore 
f-inch bars spaced 5.6 inches apart will serve the purpose. A similar 
reinforcing of bars should be placed perpendicularly to these bars. 

The above very simple solution would be theoretically accurate 
in the case of an offset 2 feet wide for the footing of a wall of indefinite 
length, assuming that the upward pressure was 7,000 pounds per 
square foot. The development of such a moment uniformly along 
the section of our square footing, implies a resistance to bending near 
the outer edges of the slab which will not actually be obtained. The 
moment will certainly be greater under the edges of the column. 
On the other hand, we have used bars in both directions. The bars 
passing under the column in each direction are just such as are re- 
quired to withstand the moment produced by the pressure on that 
part of the footing directly in front of each face of the column. It 
may be considered that the other bars have their function in tying 
the two systems into one plate whose several parts mutually support 
one another. If further justification of such a method is needed, it 
may be said that experience has shown that it practically fulfils its 
purpose. 

A more effective method of reinforcing a simple footing is shown 
in Fig. 111. Two sets of the reinforcing bars are at a-a and b-b, and 
are placed only under the column. To develop the strength of the 



234 



MASONRY AND REINFORCED CONCRETE 



corners of the footings, bars are placed diagonally across the footing, 
as at c-c and d-d. In designing this footing, the projections of the 
footing beyond the column are treated as free cantilever beams, or 
by the method discussed above. The maximum shear occurs near 
the center; and therefore, if it is necessary to take care of this shear 
by means of reinforcement, it should be provided by using stirrups. 

Example. Assume that a load of 300,000 pounds is to be carried by a 
column 28 inches square, on a soil that will safely carry a load of 6,000 pounds 
per square foot. What should be the dimensions of the footing and the size 
and spacing of the reinforcing bars? The bars are to be placed diagonally as 
well as directly across the footing, as illustrated in Fig. 111. Also investigate 
the shear. 

Solution. The load of 300,000 pounds will evidently require an 

area of 50 square feet. The sides 
of the square footing will evidently 
be 7.07 feet, or, say, 85 inches; 
and the offset on each side of the 
28-inch column is 28.5 inches. 
The area of each cantilever wing 
which is straight out from the 
column is 28.5 X 28 = 798 square 
inches = 5.54 square feet. The 
load is therefore 5.54 X 6,000 = 
33,250 pounds. Its lever-arm is 
one-half of 28.5 inches, or 14.25 
inches. The moment is therefore 
473,812 inch-pounds. Adopting the straight-line formula M c = 80bd\ 
on the basis that p = .0086,we may write the equation: 

473,812 - 80 X 28 X d 2 , 

from which, 

d 2 = 211; 
■ d = 14.5; 
A = pbd = .0086 X 28 X 14.5 
= 3.59 square inches. 

This area of metal may be furnished by eight J-inch round bars, and 
therefore there should be eight f-inch round bars spaced about 3.5 
inches apart under the column in both directions. 

The mechanics of the reinforcement of the corner sections, 
which are each 28.5 inches square, is exceedingly complicated in its 




MASONRY AND REINFORCED CONCRETE 235 

precise theory. The following approximation to it is probably 
sufficiently precise. The area of each corner section is the square 
of 28.5 inches, or 812.25 square inches. At 6,000 pounds per square 
foot, the pressure on such a section will be 33,844 pounds, and the 
center of gravity of this section is of course at the center of the square, 
which is 14.25 X 1.414 = 20.15 inches from the corner of the column. 
A bar immediately under this diagonal line would have a lever-arm of 
20.15 inches. A bar parallel to it would have the same lever-arm 
from the middle of the bar to the point were it passes under the 
column. Therefore, if we consider that this entire pressure of 
33,844 pounds has an average lever-arm of 20.15 inches, we have a 
moment of 681,957 inch-pounds. Using, as before, the moment 
equation M c = SObd 2 , we may transpose this equation to read 
b = M c -^ SOd 2 . Then, 

. , , M _ M 

= .0086 X 681 ' 957 



80 X 14.5 
= 5.06 square inches. 

This area of steel will be furnished by five l-^-inch round bars. The 
diagonal reinforcement will therefore consist of five 1^-inch round 
bars running diagonally in both directions. These bars should be 
spaced about 4 inches apart. Those that are precisely under the 
diagonal lines of the square should- be about 9 feet 8 inches long; 
those parallel to them will each be 8 inches shorter than the next bar. 
Shear. The total load of this column is 300,000 pounds. The 
shear in the footing is of course a maximum immediately under the 
edges of the column. The perimeter of the column is four times 28 
inches, or 112 inches. The thickness of the footing is something 
greater than the value found above for d (14.5 inches), and we shall 
therefore make it, say, 18 inches. This will mean that the surface 
area which would need to be punched out if the column were to shear 
its way through the footing would be 18 X 112 inches, or 2,016 square 
inches. Since the area of the column is approximately one-ninth 
of the area of the footing, the shearing force is about eight-ninths of 
the total load on a column, or it is eight-ninths of 300,000 pounds, 
which is 266,667 pounds. Dividing this by 2,016, we have about 
130 pounds per square inch as the shearing force on the concrete of 



236 MASONRY AXD REINFORCED CONCRETE 

the footing, ignoring the assistance from the 26 bars in the footing. 
There is therefore no occasion to provide for shear in such a footing. 
The intensity of the shear decreases from the maximum value just 
given, to zero at the edges of the footing. 

298. Continuous Beams. Continuous beams are sometimes 
used to save the expense of underpinning an adjacent foundation or 
wall. These footings are designed as simple beams, but the steel is 
placed in the top of the beams. 

Example. Assume that the columns on one side of a building 
are to be supported by a continuous footing; that the columns are 
22 inches square, spaced 12 feet on center; and that they support a 
load of 195,000 pounds each. If the soil will safely support 6,000 
pounds per square foot, the area required for a footing will be 195,000 
-f- 6,000 = 32.5 square feet. Since the columns are spaced 12 feet 
apart, the width of footing will be 32.5 -r- 12 = 2.71 feet, or 2 feet 
9 inches. To find the depth and amount of reinforcement necessary 
for this footing, it is designed as a simple inverted beam supported 
at both ends (the columns), and loaded with an upward pressure of 
6,000 pounds per square foot on a beam 2 feet 9 inches wide. In 
computing the moment of this beam, the continuous-beam principle 
may be utilized on all except the end spans, and thus reduce the 
moment and therefore the required dimensions of the beam. Many 
engineers ignore this principle, since it merely increases the factor of 
safety to do so. 

299. Beam Footing. When a simple footing supports a single 
column, the center of pressure of the column must pass vertically 
through the center of gravity of the footing, or there will be dangerous 
transverse stresses in the column, as discussed later. But it is some- 
times necessary to support a column on the edge of a property 
when it is not permissible to extend the foundations beyond the 
property line. In such a case, a simple footing is impracticable. The 
method of such a solution is indicated in Fig. 112, without numerical 
computation. The nearest interior column (or even a column on the 
opposite side of the building, if the building be not too wide) is 
selected, and a combined footing is constructed under both columns. 
The weight on both columns is computed. If the weights are equal, 
the center of gravity is half-way between them; if unequal, the center 
of gravity is on the line joining their centers, and at a distance from 



MASONRY AND REINFORCED CONCRETE 



237 



them such that (see Fig. 112) x:y::W 2 :W v In this case, evidently 
W 2 is the greater weight. The area abed must fulfil two conditions : 

(1) The area must equal the total loading (W 1 + W 2 ), divided by the 
allowable loading per square foot; and, 

(2) The center of gravity must be located at 0. 

An analytical solution of the relative and absolute values of a b 
and c d which will fulfil the two conditions, is very difficult, and for- 
tunately is practically unnecessary. If x and y are equal, a b c d is a 
rectangle. If W 2 is greater than 2 W v then y will be less than \x\ 
and even a triangle with the vertex under the column W ± would not 




H|F.=-— 



m 



4_1 ' J 



Mm** 






Fig. 112. Combined Footing for Two Columns, One on Edge of Property. 

fulfil the condition. In fact, if W 1 is very small compared with W 2 , it 
might be impracticable to obtain an area sufficiently large to sustain 
the weight. The proper area can be determined by a few trials, with 
sufficient accuracy for the purpose. 

The footing must be considered as an inverted beam at the 
section m n, where the moment = W 2 y — J W t y. The width is 
mn; and the required depth and the area of the steel must be com- 
puted by the usual methods. The bars will here be in the top of the 
footing, but will be bent down to the bottom under the columns, as 
shown in Fig. 112. The cross-bars under each column will be de- 



238 MASONRY AND REINFORCED CONCRETE 



signed, as in the case of the simple footing, to distribute the weight on 
each column across the width of the footing, and to transfer the weight 
to the longitudinal bars. 

RETAINING WALLS 

300. Essential Principles. The economy of a retaining wall of 
reinforced concrete lies in the fact that by adopting a skeleton form of 
construction and utilizing the tensional and transverse strength which 
may be obtained from reinforced concrete, a wall may be built, of 
"which the volume of concrete is, in some cases, not more than one- 
third the volume of a retaining wall of plain concrete which would 
answer the same purpose. Although the cost of reinforced concrete 
per cubic foot will be somewhat greater than that of plain concrete, 
it sometimes happens that such walls can be constructed for one-half 
the cost of plain concrete walls. The general outline of a reinforced- 
concrete retaining wall is similar to the letter L, the base of which is a 
base-plate made as wide as (and generally a little wider than) the 
width usually considered necessary for a plain concrete wall As a 
general rule, the width of the base should be about one-half the 
height. The face of the wall is made of a comparatively thin plate 
whose thickness is governed by certain principles, as explained later. 
At intervals of 10 feet, more or less, the base-plate and the face are 
connected by buttresses. These buttresses are very strongly fastened 
by tie-bars to both the base-plate and the face-plate. The stress in 
the buttresses is almost exclusively tension. The pressure of the 
earth tends to force the face-plate outward; and therefore the face- 
plate must be designed on the basis of a vertical slab subjected to 
transverse stresses which are maximum at the bottom and which 
reduce to zero at the top. 

If the wall is "surcharged" (which means that the earth at the 
top of the wall is not level, but runs back at a slope), then the face- 
plate will have transverse stresses even at the top. The base-plate 
is held down by the pressure of the superimposed earth. The 
buttresses must transmit the bursting pressure on the face of the wall 
backward and downward to the base-plate. The base-plate must 
therefore be designed by the same method as a horizontal slab carry- 
ing a load equal and opposite to the upward pull in each buttress. 
If the base-plate extends in front of the face of the wall, thus forming 



MASONRY AND REINFORCED CONCRETE 239 

an extended toe, as is frequently done with considerable economy 
and advantage, even that toe must be designed to withstand trans- 
verse bending at the wall line, and also shearing at that point. The 
application of these principles can best be understood by an illus- 
tration. 

301. Numerical Example. Assume that it is required to de- 
sign a retaining wall to withstand an ordinary earthwork pressure of 
20 feet, the earth being level on top. We are at once confronted with 
the determination of the actual lateral pressure of the earthwork. 
Unfortunately, this is an exceedingly uncertain quantity, depending 
upon the nature of the soil, upon its angle of repose, and particularly 
upon its condition whether wet or dry. The angle of repose is the 
largest angle with the horizontal at which the material will stand 
without sliding down. A moment's consideration will show that this 
angle depends very largely on the condition of the material, whether 
wet or dry, etc. On this account any great refinement in these calcu- 
lations is utterly useless. 

Assuming that the back face of the wall is vertical, or practically 
so; that the upper surface of the earth is horizontal; and that the 
angle of repose of the material is 30°, the total pressure of the wall 
equals | w h 2 , in which h is the total height of the wall, and w is the 
weight per unit-volume of the earth. If the angle of repose is steeper 
than this, the pressure will be less. If the angle of repose is less than 
this, the fraction ^ will be larger, but the unit-weight of the material 
will probably be smaller. Assuming the weight at the somewhat ex- 
cessive figure of 96 pounds per cubic foot, we can then say, as an 
ordinary rule, that the total pressure of the earth on a vertical strip 
of the wall one foot wide will equal 16 h 2 , in which h is the height of 
the wall in feet. The average pressure, therefore, equals 16 h; and 
the maximum pressure at a depth of h feet equals 32 h. Applying 
this figure to our numerical example, we have a total pressure on a 
vertical strip one foot wide, of 16 X 20 2 = 6,400 pounds. The pres- 
sure at a depth of 20 feet = 32 X 20 = 640 pounds. 

It is usual to compute the thickness and reinforcement of a strip 
one foot wide running horizontally between two buttresses. Prac- 
tically the strip at the bottom is very strongly reinforced by the base- 
plate, which runs at right angles to it; but if we design a strip at the 
bottom of the wall without allowing for its support from the base- 



240 MASONRY AND REINFORCED CONCRETE 



plate, and then design all the strips toward the top of the wall in the 
same proportion, the upper strips will have their proper design, while 
the lower strip merely has an excess of strength. We shall assume, 
in this case, that the buttresses are spaced 15 feet center to center. 
Then the load on a horizontal strip of face-plate 12 inches high, 15 
feet long, and 19 feet 6 inches from the top, will be 15 X 19.5 X 32, 
or 9,360 pounds. Multiplying this by 4, we have an ultimate load of 
37,440 pounds. The span in inches equals 180. Then, 

M = 37 ' 440 x 180 = 842,400 inch-pounds. 

o 

Placing this equal to 397 bd 2 , in which b = 12 inches, we find that d 2 
= 176.8, and d = 13.3 inches. At one-half the height of the wall, 
the moment will equal one-half of the above, and the required thick- 
ness d would be 9.4 inches. The actual thickness at the bottom, 
including that required outside of the reinforcement, would there- 
fore make the thickness of the wall about 16 inches at the bottom. 
At one-half the height, the thickness must be about 12 inches. 
Using a uniform taper, this would mean a thickness of 8 inches at 
the top. 

The reinforcement at the bottom would equal .0084 X 13.3 = 
.112 square inch of metal per inch of height. Such reinforcement 
could be obtained by using f-inch bars spaced 5 inches apart. The 
reinforcement at the center of the height would be .0084 X 9.4 = 
.079 square inch per inch of width. This could be obtained by using 
f-inch bars about 5 inches apart, or by using f-inch bars about 7 inches 
apart. The selection and spacing of bars can thus be made for the 
entire height. While there is no method of making a definite calcula- 
tion for the steel required in a vertical direction, it may be advisable 
to use J-inch bars spaced about 18 inches apart. 

302. Base=Plate. We shall assume that the base-plate has a 
width of one-half the height of the wall, or is 10 feet wide. If the 
inner face of the face-plate is 2 feet 6 inches from the toe, the width of 
the base-plate sustaining the earth pressure is 7 feet 6 inches. The 
actual pressure on the base-plate is that due to the total weight of the 
earth. The upward pull on the buttresses is less than this, and is 
measured by the moment of the horizontal pressure tending to tip the 
wall over. To resist this overturning tendency, there must be a down- 
ward pressure on the plate whose moment equals the moment of the 



MASONRY AND REINFORCED CONCRETE 241 

couple tending to turn the wall over. The pressure on the wall on a 

vertical strip one foot wide, as found above, is 6,400 pounds, which has 

a lever-arm, about the center of the base of the face-plate, of 6 feet 8 

inches. The vertical pressure to resist this will be applied at the 

center of the 7-foot 6-inch base, or 4 feet 5 inches from the center 

of the face-plate. The total necessary pressure will therefore be 

6,400X6.67 n „ rQ , _. 

— , or 9,o5o pounds. 1 his means an average pressure 

of 1,287 pounds per square foot. Making a similar calculation for 
this base-plate to that previously made for the face-plate, we find 
that the thickness cZ = 19.1 inches. This shows that our base-plate 
should have a total thickness of about 22 inches. 

The amount of steel per inch of width of the slab equals .0084 
X 19.1 = .160 square inch. This can be provided by J-inch bars 
spaced 4} inches apart, or by 1-inch bars spaced 6J inches apart. 
This reinforcement will be uniform across the total width of the base- 
plate. - 

303. Buttresses. The total pressure on a vertical strip one foot 
wide is 6,400 pounds. For a panel of 15 feet, this equals 96,000 
pounds; and its moment about the base of the wall equals 96,000 X 
80 inches = 7,680,000 inch-pounds. If the tie-bars in the buttresses 
are placed about 3 inches from the face of the buttresses, their distance 
from the center of the base of the face-wall will be about 89 inches. 

Therefore the tension in the bars in each buttress will equal— 

^ 8Q 

= 86,292 pounds. 

Since the earth pressures considered above are actual pressures, 
we must here consider working stresses in the metal. Allowing 
15,000 pounds' tension in "the steel, it will require 5.75 square inches 
of steel for the tie-bar of each buttress. Six 1-inch square bars will 
more than furnish this area. Even these bars need not all be extended 
to the top of the buttress, since the tension is gradually being trans- 
ferred to the face-plate. 

The width of the buttress is not very definitely fixed. It must 
have enough volume to contain the bars properly, without crowding 
them. In this case, for the six 1-inch bars, we shall make the width 
12 inches. At the base of the buttresses, these bars should be bent 
around bars running through the base-plate, so that the lower part 



242 MASONRY AND REINFORCED CONCRETE 

of the buttress will be very thoroughly anchored into the base-plate. 
It is also necessary to tie the buttress to the face-plate. The amount 
of this tension is definitely calculated for each foot of height, from 
the total pressure on the face-plate in each panel for that particular 
foot of height. At a depth of 19.5 feet, we found a bursting pressure 
of 624 pounds per square foot, or 9,360 pounds on the 15-foot panel. 
This would therefore be the required bond between the buttress and 
the face-plate at a depth of 19.5 feet. With a working tension of 
15,000 pounds per square inch, such a tension would be furnished 
by .624 square inch of metal. This equals .05 square inch of metal 
for each inch of height, and J-inch bars spaced 5 inches apart will 
furnish this tension. The amount of this tension varies from the 
above, to zero at the top of the wall. This tension is usually provided 
by small bars, such as J-inch bars, which are bent at a right angle so 
as to hook over the horizontal bars in the face-plate and run backward 
to the back of the buttress. 

In the design described above, the extension of the toe beyond the 
face of the wall is so short that there is no danger that the toe will be 
broken off on account of either shearing or transverse stress. It is 
usually good policy to place some transverse bars in the base-plate 
which are perpendicular to the face of the wall, and to have them 
extend nearly to the point of the toe. No definite calculation can be 
made of the required number of these bars, unless they are required 
to withstand transverse bending of the toe. 

If there is any danger that the subsoil is liable to settle, and thus 
produce irregular stresses on the base-plate, a large reinforcement in 
this direction may prove necessary. It is good policy to place at least 
J-inch bars every 12 inches through the base-plate, for the prevention 
of cracks; and this amount should be increased as the uncertainty in 
the stress in the base-plate increases. Although there are no definite 
stresses in the top of the wall, it is usual to make the thickness of the 
face-plate at least 6 inches at the top, and also to place a finishing 
cornice on top of the wall, somewhat as is shown in Fig. 113. 

When the subsoil is very unreliable, it is even possible that there 
might be a tendency for the front and back of the base-plate to sink, 
and to break the base-plate by tension of the top. This can be re- 
sisted by bars in the upper part of the base-plate which are perpen- 
dicular to the wall. 



MASONRY AND REINFORCED CONCRETE 



243 



304. L=Shaped Retaining Walls. Retaining walls of very 
moderate height may be constructed in L-shaped sections without 
buttresses, by thickening the walls at the base, and by using suffi- 
cient reinforcement to resist the transverse stresses, which, of course, 
have their maximum value at the base of the wall (Fig. 114). From 
the standpoint of cubic yards of concrete and pounds of steel, such a 

12'U- 




<-2-e» 



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ID. §p. 



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Fig. 113. Section and Plan of Retaining Wall, Showing Reinforcement. 

wall is not as economical as the buttressed wall, but the forms are very 
much more simple and are less expensive. A low wall is always made 
much thicker than mere theoretical computation would call for, and in 
such a case the additional thickening for the L design might be little or 
nothing. For high walls — twenty feet or more — the economy 
utterly disappears. The mechanics of this form of wall is quite 
different from the form with buttresses. In the case of a buttressed 
wall, the vertical plate between the buttresses is merely designed to 
resist the bursting pressure on a slab which has the buttresses as 
abutments. When there are no abutments, the pressure on each 
unit vertical strip of the wall must be computed; and the strength 



244 



MASONRY AND REINFORCED CONCRETE 



hor. bars^'tf 



at every section (vertically) must be computed on the basis of a 
cantilever acted on by horizontal forces. This practically means that 
the moment increases from zero at the top of the wall to a maximum 
at the base just above the base-plate. Of course the mechanics of 
the wall taken as a whole, in its pressure on the subsoil, is identical 
with that of the other form of retaining wall. 

WIND BRACING 
305. General Principles. The practical applications of the 
principles of reinforced concrete which have already been discussed, 

have been almost exclusively those 
required for sustaining vertical loads ; 
but a structure consisting simply of 
beams, girders, slabs, and columns 
may fall down, like a house of cards, 
unless it is provided with lateral 
bracing to withstand wind pressure 
and any lateral forces tending to 
turn it over. The necessary provis- 
ion for such stresses is usually made 
by placing brackets in the angles 
between posts and girders, as has 
been illustrated in Fig. 102. These 
brackets are reinforced with bars 
which will resist any tensile stress 
on the brackets. The compressive 
strength of concrete may be relied on 
to resist a tendency to crush the 
brackets by compression. Usually 
such brackets will occur in' pairs at 
each end of a beam supported on two 
columns. If we consider that any given moment is to be divided 
equally between two brackets, then, if we are to have a working ten- 
sion of 15,000 pounds per square inch in the steel, and a working 
compression^ 500 pounds per square inch in the concrete, the area 
of the concrete must be 30 times the area of the steel. But since the 
outer face of the concrete will have practically twice the compression 
of the concrete at the angle of the beam and column, and since the 
maximum of 500 pounds per square inch must not be exceeded, we 




Fig. 1 14. L-Shaped Retaining Wall. 



MASONRY AND REINFORCED CONCRETE 245 



must have twice that area of concrete; or, in other words, the area 
of tiie concrete from the point of the angle down to the face must be 
CO times the area of the steel. 

Although these brackets are frequently put in without any defi- 
nite design, it is possible to make some sort of computation, especially 
when a building is directly exposed to wind pressure, by computing 
the moment of the wind pressure. For example, if a building is 
100 feet long and 50 feet high, and is subjected to a wind pressure of 
30 pounds per square foot, the total wind pressure will be 50 X 100 
X 30 = 150,000 pounds. Considering the center of pressure as 
applied at half the height, this would give a moment about the base 
of the building, of 150,000 X 25 = 3,750,000 foot-pounds = 45,000,- 
000 inch-pounds. If this 100-foot building had eight lines of columns 
with a pair of brackets on each line, and was four stories high, there 
would be 64 such brackets to resist wind pressure. Each bracket 
would therefore be required to resist -fa of 45,000,000 inch-pounds, 
or about 700,000 inch-pounds. We shall assume that the bracket 
will have a depth of 25 inches, from the intersection of the center lines 
of the column and the beam to the steel near the face of the bracket. 
Then, since each bracket must withstand a moment of 700,000 inch- 
pounds, the stress in the steel will be 700,000 -f- 25 = 28,000 pounds. 
If the actual stress in the steel is 15,000 pounds per square inch, this 
would require 1.87 square inches of steel, which would be more than 
supplied by four f inch square bars. If these brackets were 12 inches 
wide and 25 inches deep, the area of concrete is 300 square inches, 
which is 160 times the area of the steel. There is, therefore, an ample 
amount of concrete to withstand compression, on the part of those 
brackets which are subject to compression rather than tension. It is 
probable that the above calculation is excessive on the side of safety, 
since it is quite improbable that such a broad area would ever be 
subject to a pressure of 30 pounds per square foot over the whole area. 
The method of calculation also ignores the fact that the monolithic 
character of a reinforced-concrete structure furnishes a very consider- 
able resistance at the junction of columns and girders, and that they 
should not by any means be considered as if they were pin-connected 
structures, which would require that the whole of the lateral stiffen- 
ing should be supplied by these brackets. Nevertheless these brackets 
must be designed according to some such method. 



246 MASONRY AND REINFORCED CONCRETE 

VERTICAL WALLS 

306. Curtain Walls. Vertical walls which are not intended to 
carry any weight, are sometimes made of reinforced concrete. They 
are then called curtain walls, and are designed merely to fill in the 
panels between the posts and girders which form the skeleton frame of 
the building. When these walls are interior walls, there is no definite 
stress which can be assigned to them, except by making assumptions 
that may be more or less unwarranted. WTien such walls are used 
for exterior walls of buildings, they must be designed to withstand 
wind pressure. This wind pressure will usually be exerted as a 
pressure from the outside tending to force the wall inward; but if 
the wind is in the contrary direction, it may cause a lower atmospheric 
pressure on the outside, while the higher pressure of the air within 
the building will tend to force the wall outward. It is improbable, 
however, that such a pressure would ever be as great as that tending 
to force the wall inward. Such walls may be designed as slabs 
carrying a uniformly distributed load, and supported on all four sides. 
If the panels are approximately square, they should have bars in both 
directions, and should be designed by the same method as "slabs 
reinforced in both directions," as has previously been explained. 
If the vertical posts are much closer together than the height of the 
floor, as sometimes occurs, the principal reinforcing bars should be 
horizontal, and the walls should be designed as slabs having a span 
equal to the distance between the posts. Some small bars spaced 
about 2 feet apart should be placed vertically to prevent shrinkage. 
The pressure of the wind corresponding to the loading of the slab, 
is usually considered to be 30 pounds per square foot, although the 
actual wind pressure will very largely depend on local conditions, 
such as the protection which the building receives from surrounding 
buildings. A pressure of thirty pounds per square foot is usually 
sufficient; and a slab designed on this basis will usually be so thin, 
perhaps only 4 inches, that it is not desirable to make it any thinner. 
Since designing such walls is such an obvious application of the 
equations and problems already solved in detail, no numerical illus- 
tration will here be given. 



MASONRY AND REINFORCED CONCRETE 247 

CULVERTS 

307. Box Culverts. The permanency of concrete,, and par- 
ticularly reinforced concrete, has caused its adoption in the construc- 
tion of culverts of all dimensions, from a cross-sectional area of a very 
few square feet, to that of an arch which might be more properly 
classified under the more common name masonry arch. The smaller 
sizes can be constructed more easily, and with less expense for the 
forms, by giving them a rectangular cross-section. The question of 
foundations is solved most easily by making a concrete bottom, as 
well as side walls and top. The structure then becomes literally a 
box. Its design consists in the determination of the external pressure 
exerted by the earth, and of the required thickness of the concrete to 
withstand the pressure on the flat sides considered as slabs. The 
most uncertain part of the computation lies in the determination of 
the actual pressure of the earth. Under the heading ' 'Retaining 
Walls," this uncertainty was discussed. 

One very simple method is to assume that the earth pressure is 
equivalent to that of a liquid having a unit-weight equal to that 
of the weight of a cubic foot of the earth, which is nearly 100 pounds. 
Under almost any circumstances, these figures would be sufficiently 
large, and perhaps very excessive. Calculations on such a basis are 
therefore certainly safe. If the pressure is computed on this basis, 
and a factor of safety of 2 is used, it is equivalent to an actual pressure 
of only one-half the amount (which is more probable), having a factor 
of 4. If the depth of the earth is quite large compared with the 
dimensions of the culvert, we may consider that the upward pressure 
on the bottom, as well as the lateral pressure on the sides, is prac- 
tically the same as the downward pressure on the top. If the bottom 
of the culvert is laid on rock, or on soil which is practically unyielding, 
there will be no necessity of considering that there is any upward 
pressure on the bottom slab tending to burst that slab upward. The 
softer the soil, the greater will be the tendency to transverse bending 
in the bottom slab. 

Since the design of rectangular box culverts is purely an applica- 
tion of the equations for transverse bending, after the external pres- 
sures have been determined, no numerical example will here be given. 
These structures are not only reinforced with bars, considering the 



248 



MASONRY AND REINFORCED CONCRETE 



sides as slabs, but should also have bars placed across the corners, 
which will withstand a tendency of the section to collapse in case 
the pressure on opposite sides is unequal. They must also be rein- 
forced with bars running longitudinally with the culvert. As in the 
other cases of longitudinal reinforcement, no definite design can be 
made for its amount. A typical cross-section for such a culvert is 
shown in Fig. 115. The longitudinal bars are indicated in this figure. 
They are used to prevent cracks owing to expansion or contraction, 
and also to resist any tendency to rupture which might be caused by 
a settling or washing-out of the subsoil for any considerable distance 
under the length of the culvert. 




pL uiq ^u,, 4,-aJ 



i _j i i i i i 

-th— r-r i r- r 



.-!Trr 



rET 



i i 



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Longitudinal Section 




Hglf End Elevation and Section 




I I I I I M I I I I I I I I I I I I I I I 



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Half Plan 



Fig. 115. Rectangular Box Culvert. 

308. Arch Culverts. The general subject of arches, and 
especially the application of reinforced concrete to arch construction, 
are taken up in Part V, and therefore will not be further discussed 
here. 

COLUMNS 

.300. Methods of Reinforcement. The laws of mechanics, as 
well as experimental testing on full-sized columns of various structural 
materials, show that very short columns, or even those whose length 
is ten times their smallest diameter, w T ill fail by crushing or shearing 



MASONRY AND REINFORCED CONCRETE 249 

of the material. If the columns are very long, say twenty or more 
times their smallest diameter, they will probably fail by bending, 
which will produce an actual tension on the convex side of the column. 
The line of division between long- and short columns is practically 
very uncertain, owing to the fact that the center line of pressure of a 
column is frequently more or less eccentric because of irregularity 
of the bearing surface at top or bottom. Such an eccentric action 
w T ill cause buckling of the column, even when its length is not very 
great. On this account, it is always wise (especially for long columns) 
to place reinforcing bars within the column. The reinforcing bars 
consist of longitudinal bars (usually four, and sometimes more with 
the larger columns), and bands of small bars spaced from 6 to 18 
inches apart vertically, which bind together the longitudinal bars. 
The longitudinal bars are used for the purpose of providing the 
necessary transverse strength to prevent buckling of the column. 
As it is practically impossible to develop a satisfactory theory on 
which to compute the required tensional strength in the convex side 
of a column of given length, without making assumptions which are 
themselves of doubtful accuracy, no exact rules for the sizes of the 
longitudinal bars in a column will be given. The bars ordinarily 
used vary from ^ inch square to 1 inch square; and the number is 
usually four, unless the column is very large (400 square inches or 
larger) or is rectangular rather than square. It has been claimed by 
many, that longitudinal bars in a column may actually be a source of 
danger, since the buckling of the bars outward may tend to disinte- 
grate the column. This buckling can be avoided, and the bars made 
mutually self-supporting, by means of the bands which are placed 
around the column. These bands are usually J-inch or f-inch round 
or square bars. The specifications of the Prussian Public Works 
for 1904 require that these horizontal bars shall be spaced a distance 
not more than 30 times their diameter, which would be 1\ inches for 
}-inch bars, and \\\ inches for f-inch bars. The bands in the column 
are likewise useful to resist the bursting tendency of the column, 
especially when it is short. They will also reinforce the column 
against the tendency to shear, which is the method by which failure 
usually takes place. The angle between this plane of rupture and a 
plane perpendicular to the line of stress, is stated to be 60°. If, 
therefore, the bands are placed at a distance apart equal to the 



250 MASONRY AND REINFORCED CONCRETE 

smallest diameter of the column, any probable plane of rupture will 
intersect one of the bands, even if the angle of rupture is somewhat 
smaller than 60°. 

The unit working pressure permissible in concrete columns is 
usually computed at from 350 to 500 pounds per square inch. The 
ultimate compression for transverse stresses for 1:3:5 concrete has 
been taken at 2,000 pounds per square inch. With a factor of 4, this 
gives a working pressure of 500 pounds per square inch; but the 
ultimate stress in a column of plain concrete is generally less than 
2,000 pounds per square inch. Tests of a large number of 12 by 12- 
inch plain concrete columns showed an ultimate compressive strength 
of approximately 1,000 pounds per square inch; but such columns 
generally begin to fail by the development of longitudinal cracks. 
These would be largely prevented by the use of lateral reinforcement 
or bands. Therefore the use of 500 pounds per square inch as a 
working stress for columns which are properly reinforced, may be 
considered justifiable although not conservative. 

310. Design of Columns. It may be demonstrated by theoreti- 
cal mechanics, that if a load is jointly supported by two kinds of 
material with dissimilar elasticities, the proportion of the loading 
borne by each will be in a ratio depending on their relative areas and 
moduli of elasticity. The formula for this may be developed as 
follows : 

C = Total unit-compression upon concrete and steel in pounds per 
square inch = Total load divided by the combined area of the con- 
crete and the steel; 

c = Unit-compression in the concrete, in pounds per square inch; 

s = Unit-compression in the steel, in pounds per square inch; 

p = Ratio of area of steel to total area of column; 

jp 
r = ^ s = Ratio of the moduli of elasticity; 

e s = Deformation per unit of length in the steel; 

e = Deformation per unit of length in the concrete; 
A s = Area of steel; 
A c = Area of concrete. 

The total compressive force in the concrete = A c X c; and that 
in the steel = A s X s. 

The sum of these compressions = the total compression; and 

therefore, 

C (A c + A s ) = A c c + A B s. 



MASONRY AND REINFORCED CONCRETE 251 

The actual linear compression of the concrete equals that of the 
steel; therefore, 

c s 

E a E s . 

E 

From this equation, since r = -yf, we may write the equation rc = s. 

Solving the above equation for 0, we obtain : 

_ A c c -\~ A s s - 
A c + A s * 

Substituting the value of s = re, we have: 

n /Ac + A s rs /A s + A c - A s + A s r N 

If p = the ratio of cross-section of steel to the total cross-section of 
the column, we have : 

As 

P A c + As * 

Substituting this value of — — *-— in the above equation, we may 
write: 

C = c ( 1 — p + pr) . 

Solving this equation for p, we obtain : 



P = 



(41) 



c(r-l) 

Example 1. A column is designed to carry a load of 160,000 pounds. 
If the column is made 18 inches square, and the load per square inch to be 
carried by the concrete is limited to 400 pounds, what must be the ratio of the 
steel, and how much steel would be required? 

Answer. A column 18 inches square has an area of 324 square 

inches. Dividing 160,000 by 324, we have 494 pounds per square 

inch as the total unit-compression upon the concrete and the steel, 

which is C in the above formula. Assume that the concrete is 1:3:5 

concrete, and that the ratio of the moduli of elasticity (r) is therefore 

12. Substituting these values in Equation 41 , we have : 

494-400 noi . 

^ 4oo ( i2-ir - 0214 - 

Multiplying this ratio by the total area of the column, 324 square 
inches, we have 6.93 square inches of steel required in the column. 
This would very nearly be provided by four bars \\ inches square. 
Four round bars \\ inches in diameter would give an excess in area. 



252 MASONRY AND REINFORCED CONCRETE 

Either solution would be amply safe under the circumstances, pro- 
vided the column was properly reinforced with bands. 

Example 2. A column 16 inches square is subjected to a load of 115,000 
pounds, and is reinforced by four 1-inch square bars besides the bands. What 
is the actual compressive stress in the concrete per square inch? 

Answer. Dividing the total stress (115,000) by the area (256), 
we have the combined unit-stress C = 449 pounds per square inch. 
By inverting one of the equations above, we can write : 

C 

c = . 

1 — p + r p 

In the above case, the four J-inch bars have an area of 3.06 sauare 
inches; and therefore, 

Substituting these values in the above equation, we may write: 

449 449 



1 - .012 + (.012 X 12) 1 .132 



397 pounds per square inch. 



The net area of the concrete in the above problem is 252.94 square 
inches. Multiplying this by 397, we have the total load carried by 
the concrete, which is 100,117 pounds. Subtracting this from 
115,000 pounds, the total load, we have 14,883 pounds as the com- 
pressive stress carried by the steel. Dividing this by 3.06, the area 
of the steel, we have 4,864 pounds as the unit compressive stress in the 
steel. This is practically twelve times the unit-compression in the 
concrete, which is an illustration of the fact that if the compression 
is shared by the two materials in the ratio of their moduli of elasticity, 
the unit-stresses in the materials will be in the same ratio. This unit- 
stress in the steel is about one-third of the working stress which may 
properly be placed on the steel. It shows that we cannot economically 
use the steel in order to reduce the area of the concrete, and that 
the chief object in using steel in the columns is in order to protect 
the columns against buckling, and also to increase their strength by 
the use of bands. 

It sometimes happens that in a building designed to be struc- 
turally of reinforced concrete, the column loads in the columns of the 
lower story may be so very great that concrete columns of sufficient 
size would take up more space than it is desirable to spare for such 



MASONRY AND REINFORCED CONCRETE 253 

a purpose. For example, it might be required to support a load of 
320,000 pounds on a column 18 inches square. If the concrete 
(1:3:5) is limited to a compressive stress of 400 pounds per square 
inch, we may solve for the area of steel required, precisely as was done 
in example 1. We should find that the required percentage of steel 
was 13.4 per cent, and that the required area of the steel was therefore 
43.3 square inches. But such an area of steel could carry the entire 
load of 320,000 pounds without the aid of the concrete, and would 
have a compressive unit-stress of only 7,400 pounds. In such a case, 
it would be more economical to design a steel column to carry the 
entire load, and then to surround the column with sufficient concrete 
to fireproof it thoroughly. Since the stress in the steel and the con- 
crete are divided in proportion to their relative moduli of elasticity, 
which is usually about 10 or 12, we cannot develop a working stress 
of, say, 15,000 pounds per square inch in the steel, without at the 
same time developing a compressive stress of 1,200 to 1,500 pounds in 
the concrete, which is objectionably high as a working stress. 

311. . Hooped Columns. It has been found that the strength of 
a column is very greatly increased and even multiplied by surrounding 
the column by numerous hoops or bands or by a spiral of steel. The 
basic principle of this strength can best be appreciated by considering 
a section of stovepipe filled with sand and acting as a column. The 
sand alone, considered as a column, would not be able to maintain 
its. form, much less to support a load, especially if it was dry. But 
when it is confined in the pipe, the columnar strength is very con- 
siderable. Concrete not only has great crushing strength, even when 
plain, but can also be greatly strengthened against failure by the 
tensile strength of bands which confine it. The theory of the 
amount of this added resistance is very complex, and will not here be 
given. The general conclusions, in which experimental results sup- 
port the theory, are as follows : 

1. The deformation of a hooped column is practically the same as that 
of a plain concrete column of equal size for loads up to the maximum for a 
plain column. 

2. Further loading of a hooped column still further increases the shorten- 
ing and swelling of the column, the bands stretching out, but without causing 
any apparent failure of the column. 

3. Ultimate failure occurs when the bands break or, having passed 
their elastic limit, stretch excessively. 



254 MASONRY AND REINFORCED CONCRETE 



Hooped columns may thus be trusted to carry a far greater unit- 
load than plain columns, or even columns with longitudinal rods and a 
few bands. There is one characteristic that is especially useful for 
a column which is at all liable to be loaded with a greater load than its 
nominal loading. A hooped column will shorten and swell very 
perceptibly before it is in danger of sudden failure, and will thus give 
ample warning of an overload. 

Considere has developed an empirical formula based on actual 
tests, for the strength of hooped columns, as follows : 

Ultimate strength = c'A + 2As'pA (42) 

in which, 

c' = Ultimate strength of the concrete; 

s' = Elastic limit of the steel ; 

p = Ratio of area of the steel to the whole area;* 

A = Whole area of the column. 

This formula is applicable only for reinforcement of mild steel: 
Applying this formula to a hooped column tested to destruction by 
Professor Talbot, in which the ultimate strength (V) of similar con- 
crete was 1,380 pounds per square inch, the elastic limit of the steel 
(V) was 48,000 pounds per square inch; the ratio of reinforcement 
(p) was .0212; and the area (A) was 104 square inches; and sub- 
stituting these quantities in Equation 42, we have, for the computed 
ultimate strength, 409,900 pounds. The actual ultimate by Talbot's 
test was 351,000 pounds, or about 86 per cent. 

Talbot has suggested the following formulae for the ultimate 
strength of hooped columns per square inch : 

Ultimate strength = 1,600 + 65,000 p (for mild steel) • (43) 
= 1,600 + 100,000 p (for high steel) ■ -(44) 

In these formulae, p applies only to the area of concrete within the 
hooping; and this is unquestionably the correct principle, as the 
concrete outside of the hooping should be considered merely as fire 
protection and ignored in the numerical calculations, just as the con- 
crete below the reinforcing steel of a beam is ignored in calculating 
the strength of the beam. The ratio of the area of the steel is com- 
puted by computing the area of an equivalent thin cylinder of steel 
which would contain as much steel as that actually used in the bands 
or spirals. For example, suppose that the spiral reinforcement con- 



MASONRY AND REINFORCED CONCRETE 255 

sisted of a J-inch round rod, the spiral having a pitch of 3 inches. 
A J-inch round rod has an area of .196 square inch. That area for 3 
inches in height would be the equivalent of a solid band .0653 inch 
thick. If the spiral had a diameter of, say, 11 inches, its circum- 
ference would be 34.56 inches, and the area of metal in a horizontal 
section would be 34.56 X .0653 = 2.257 square inches. The area 
of the concrete within the spiral is 95.0 square inches. The value of 
p is therefore 2.257 -r- 95.0 = .0237. If the J-inch bar were made of 
high-carbon steel, the ultimate strength per square inch of the column 
would be 1,600 + (100,000 X .0237) = 1,600 + 2,370 = 3,970. 
The unit-strength is considerably more than doubled. The ultimate 
strength of the whole column is therefore 95 X 3,970 = 377,150 
pounds. Such a column could be safely loaded with about 94,300 
pounds, provided its length was not so great that there was danger of 
buckling. In such a case, the unit-stress should be reduced according 
to the usual ratios for long columns, or the column should be liberally 
reinforced with longitudinal rods, which would increase its transverse 
strength. 

312. Effect of Eccentric Loading of Columns. It is well 
known that if a load on a column is eccentric, its strength is consider- 
ably less than when the resultant line of pressure passes through the 
axis of the column. The theoretical demonstration of the amount of 
this eccentricity depends on assumptions which may or may not be 
found in practice. The following formula is given without proof or 
demonstration, in Taylor and Thompson's treatise on Concrete: 

Let e = Eccentricity of load; 
b = Breadth of column; 
/ — Average unit-pressure; 

/' = Total unit-pressure of outer fibre nearest to line of vertical 
pressure 
Then, 

r-/(i+£) ( 45 > 

As an illustration of this formula, if the eccentricity on a 12-inch 
column were 2 inches, we should have b = 12, and e = 2. Sub- 
stituting these values in Equation 45, we should have f = 2 /, which 
means that the maximum pressure would equal twice the average 
pressure. In the extreme case, where the line of pressure came to 
the outside of the column, or when e = \ b, we should have that the 



256 MASONRY AND REINFORCED CONCRETE 

maximum pressure on the edge of the column would equal four times 
the average pressure. 

Any refinements in such a calculation, however, are frequently 
overshadowed by the uncertainty of the actual location of the center 
of pressure. A column which supports two equally loaded beams 
on each side, is probably loaded more symmetrically than a column 
which supports merely the end of a beam on one side of it. The 
best that can be done is arbitrarily to lower the unit-stress on a column 
which is probably loaded somewhat eccentrically. 

TANKS 

313. Design. The extreme durability of reinforced-concrete 
tanks, and their immunity from deterioration by rust, which so 
quickly destroys steel tanks, have resulted in the construction of a 
large and increasing number of tanks in reinforced concrete. Such 
tanks must be designed to withstand the bursting pressure of the 
water. If they are very high compared with their diameter, it is 
even possible that failure might result from excessive wind pressure. 

The method of designing one of these tanks may best be con- 
sidered from an example. Suppose that it is required to design a 
reinforced-concrete tank with a capacity of 50,000 gallons, which shall 
have an inside diameter of 18 feet. At 7.48 gallons per cubic foot, 
a capacity of 50,000 gallons will require 6,684 cubic feet. If the inside 
diameter of the tank is to be 18 feet, then the 18-foot circle will con- 
tain an area of 254.5 square feet. The depth of the water in the 
tank will therefore be 26.26 feet. The lowest foot of the tank will 
therefore be subjected to a bursting pressure due to 25.76 vertical 
feet of water. Since the water pressure per square foot increases 62 h 
pounds for each foot of depth, we shall have a total pressure of 1,610 
pounds per square foot on the lowest foot of the tank. Since the 
diameter is 18 feet, the bursting pressure it must resist on each side 
is one-half of 18 X 1,610 = i X 28,980 = 14,490 pounds. If we 
allow a working stress of 15,000 pounds per square inch, this will 
require .966 square inch of metal in the lower foot. Since the bursting 
pressure is strictly proportional to the depth of the water, we need 
only divide this number proportionally to the depth to obtain the 
bursting pressure at other depths. For example, the ring one foot 
high, at one-half the depth of the tank, should have .483 square inch 



Masonry and reinforced concrete 257 

of metal; and that at one-third of the depth, should have .322 square 
inch of metal. The actual bars required for the lowest foot may be 
figured as follows: .966 square inch per foot equals .0805 square 
inch per inch; f-inch square bars, having an area .5625 square inch, 
will furnish the required strength when spaced 7 inches apart. At 
one-half the height, the required metal per linear inch of height is 
half of the above, or .040. This could be provided by using f-inch 
bars spaced 14 inches apart; but this is not so good a distribution of 
metal as to use f-inch square bars having an area of .39 square inch, 
and to space the bars nearly 10 inches apart. It would give a still 
better distribution of metal, to use J-inch bars spaced 6 inches apart 
at this point, although the J-inch bars are a little more expensive per 
pound, and, if they are spaced very closely, will add slightly to the 
cost of placing the steel. The size and spacing of bars for other points 
in the height can be similarly determined. 

A circle 18 feet in diameter has a circumference of somewhat 
over 56 feet. Assuming as a preliminary figure that the tank is 
to be 10 inches thick at the bottom, the mean diameter of the base 
ring would be 18.83 feet, which would give a circumference of over 
59 feet. Allowing a lap of 3 feet on the* bars, this would require 
that the bars should be about 62 feet long. Although it is possible 
to have bars rolled of this length,, they are very difficult to handle, 
and require to be transported on the railroads on two flat cars. It is 
therefore preferable to use bars of slightly more than half this length, 
and to make two joints in each band. 

The bands which are used for ordinary wooden tanks are usually 
fastened at the ends by screw-bolts. Some such method is necessary 
for the bands of concrete tanks, provided the bands are made of plain 
bars. Deformed bars have a great advantage in such work, owing to 
the fact that, if the bars are overlapped from 18 inches to 3 feet, 
according to their size, and are then wired together, it will require a 
greater force than the strength of the bar to pull the joints apart after 
they are once thoroughly incased in the concrete and the concrete 
has hardened. 

314. Test for Overturning. Since the computed depth of the 
water is over 26 feet, we must calculate that the tank will be, say, 28 
feet high. Its outer diameter will be approximately 20 feet. The 
total area exposed to the surface of the wind, will be 560 square feet. 



258 MASONRY AND REINFORCED CONCRETE 

We may assume that the wind has an average pressure of 50 pounds 
per square foot; but owing to the circular form of the tank, we shall 
assume that its effective pressure is only one-half of this; and there- 
fore we x may figure that the total overturning pressure of the wind 
equals 500 X 25 = 14,000 pounds. If this is considered to be applied 
at a point 14 feet above the ground, we have an overturning moment 
of 196,000 foot-pounds, or 2,352,000 inch-pounds. 

Although it is not strictly accurate to consider the moment of 
inertia of this circular section of the tank as it would be done if it were 
a strictly homogeneous material, since the neutral axis, instead of 
being at the center of the section, will be nearer to the compression 
side of the section, our simplest method of making such a calculation 
is to assume that the simple theory applies, and then to use a generous 
factor of safety. The effect of shifting the neutral axis from the 
center toward the compression side, will be to increase the unit-com- 
pression on the concrete, and reduce the unit-tension in the steel ; but, 
as will be seen, it is generally necessary to make the concrete so thick 
that its unit compressive stress is at a very safe figure, while the 
reduction of the unit-tension in the steel is merely on the side of safety. 

Applying the usual theory, we have, for the moment of inertia of 
a ring section, .049 (d^ — d 4 ). Let us assume as a preliminary 
figure, that the wall of the tank is 10 inches thick at the bottom. 
Its outside diameter is therefore 18 feet + twice 10 inches, or 236 
inches. The moment of inertia I = .049 (236 4 - 216 4 ) = 45,337,- 
842 biquadratic inches. Calling c the unit-compression, we have, as 
the ultimate moment due to wind pressure: 

cl c X 45,337,842 ooco '. , , 

M = t— j- = r— t = 2,352,000 men-pounds, 

\ di h di 

in which \d x = 118 inches. 

Solving the above equation for c, we have c equals a fraction 
less than 6 pounds per square inch. This pressure is so utterly 
insignificant, that, even if we double or treble it to allow for the shift- 
ing of the neutral axis from the center, and also double or treble the 
allowance made for wind pressure, although the pressure chosen is 
usually considered ample, we shall still find that there is practically 
no danger that the tank will fail owing to a crushing of the concrete 
due to wind pressure. 



MASONRY AND REINFORCED CONCRETE 259 

The above method of computation has its value in estimating 
the amount of steel required for vertical reinforcement. On the basis 
of 6 pounds per square inch, a sector with an average width of 1 inch 
and a diametral thickness of 10 inches would sustain a compression 
of about 60 pounds. Since we have been figuring working stresses, 
we shall figure a working tension of, say, 16,000 pounds per square 

inch in the steel. This tension would therefore require tttt^tt = 

.0037 square inch of metal per inch of width. Even if |-inch bars 
were used for the vertical reinforcement, they would need to be 
spaced only about 17 inches apart. This, however, is on the basis 
that the neutral axis is at the center of the section, which is known to 
be inaccurate. 

A theoretical demonstration of the position of the neutral axis 
for such a section, is so exceedingly complicated that it will not be 
considered here. The theoretical amount of steel required is always 
less than that computed by the above approximate method; but the 
necessity for preventing cracks, which would cause leakage, would 
demand more vertical reinforcement than would be required by wind 
pressure alone. 

315. Practical Details of the Above Design. It was assumed 
as an approximate figure, that the thickness of the concrete side wall 
at the base of the tank should be 10 inches. The calculations have 
shown that, so far as wind pressure is concerned, such a thickness is 
very much greater than is required for this purpose; but it will not 
do to reduce the thickness in accordance with the apparent require- 
ments for wind pressure. Although the thickness at the bottom might 
be reduced below 10 inches, it probably would not be wise to do so. 
It may, however, be tapered slightly towards the top, so that at the 
top the thickness will not be greater than 6 inches, or perhaps even 
5 inches. The vertical bars in the lower part of the side wall must be 
bent so as to run into the base slab of the tank. This will bind the 
side wall to the bottom. The necessity for reinforcement in the 
bottom of the tank depends very largely upon the nature of the 
foundation, and also to some extent on the necessity for providing 
against temperature cracks, as has been discussed in a previous sec- 
tion. Even if the tank is placed on a firm and absolutely unyielding 
foundation, some reinforcement should be used in the bottom, in 



260 MASONRY AND REINFORCED CONCRETE 

order to prevent cracks which might produce leakage. These bars 
should run from a point near the center, and be bent upward at least 
2 or 3 feet into the vertical wall. Sometimes a gridiron of bars 
running in both directions is used for this purpose. This method is 
really preferable to the radial method. The methods of making 
tanks water-tight have already been discussed. 




Large Concrete Sewer in Aramingo Canal. 




Wakeling Street Concrete Sewer, 16 ft. by 10 ft. 6 in. 



TWO VIEWS OF SEWERS IN THE CITY OF PHILADELPHIA, PA. 

Courtesy of Geo. S. Webster, Chief Engineer, Bureau of Surveys, Dept, of Public Works. 



MASONRY AND REINFORCED 
CONCRETE 



PART IV 



FINISHING SURFACES OF CONCRETE 

316. Imperfections. To give a satisfactory finish to exposed 
surfaces of concrete is a rather difficult problem. Usually, when 
the forms are taken down, the surface of the concrete shows the 
joints, knots, and grain of the wood. It has more the appearance of 
a piece of rough carpentry work than that of finished masonry. Or, 
failure to tamp or flat-spade the surfaces next to the forms, will result 
in rough places or stone pockets. Lack of homogeneity in the concrete 
will cause a variation in the surface texture of the concrete. Varia- 
tion of color, or discoloration, is one of the most common imperfec- 
tions. Old concrete adhering to the forms will leave pits in the 
surface; or the pulling-ofT of the concrete in spots, as a result of it 
adhering to the forms when they are removed, will cause a roughness. 

To guard against these imperfections, the forms must be well 
constructed of dressed lumber, and the pores should be well filled 
with soap or paraffine. The concrete should be thoroughly mixed, 
and, when placed, care should be taken to compact the concrete 
thoroughly, next to the forms. The variation in color is usually 
due to the leaching-out of lime, which is deposited in the form of an 
efflorescence on the surface; or to the use of different cements in adja- 
cent parts of the same work. The latter case usually can be avoided 
by using the same brand of cement on the entire work, and the 
former will be treated under the heading of Efflorescence (Article 329). 

317. Plastering. Plastering is not usually successful, although 
there are cases where a mixture of equal parts of cement and sand 
has apparently been successful; and when finished rough, it did not 
show any cracks. It is generally considered impossible to apply 
mortar in thin layers to a concrete surface, and make it adhere for any 

Copyright, 1908, by American School of Correspondence 



262 MASONRY AND REINFORCED CONCRETE 

length of time. When the plastering begins to scale off, it looks 
worse than the unfinished surface. This paragraph is intended more 
as a warning against this manner of finishing concrete surfaces than 
as a description of it as an approved method of finish. 

318. Mortar Facing. The following method has been adopted 
by the New York Central Railroad for giving a good finish to exposed 
concrete surfaces : 

The forms of 2-inch tongued-ancl-grooved pine were coated with 
soft soap, all openings hi the joints of the forms being filled with hard 
soap. The concrete was then deposited, and, as it progressed, was 
drawn back from the face with a square-pointed shovel, and 1 : 2 mor- 
tar poured in along the forms. When the forms were removed, and 
while the concrete was green, the surface was rubbed, with a circular 
motion, with pieces of white firebrick, or brick composed of one part 
cement and one part sand. The surface was then dampened and 
painted with a 1 : 1 grout, rubbed in, and finished with a wooden 
float, leaving a smooth and hard surface when dry. 

The following method of placing mortar facing has been found 
very satisfactory, and has been adopted very extensively in the last 
few years: A sheet-iron plate 6 or 8 inches wide and about 5 or 6 
feet long, has riveted across it on one side angles of f -inch size, or such 
other size as may be necessary to give the desired thickness of mortar 




5-0"- 



7 



I I 1 TT — ' III 

i p, I pi J jo, 

licsris zvctoc. fa' ^ p/dte & 

ihi 'pi IQ Ip; 

Fig. 1 1 6. Mould for Mortar Facing. 

facing, these angles being spaced about two feet apart (Fig 116) . In 
operation, the ribs of the angles are placed against the forms; and the 
space between the plate and forms is filled with mortar, which is mixed 
in small batches, and thoroughly tamped. The concrete back-filling is 
then placed; the mould is withdrawn; and the facing and back- 
filling are rammed together. The mortar facing is mixed in the pro- 
portion of one part cement, to 1, 2, or 3 parts sand; usually a 1 : 2 
mixture is employed, mixed wet and in small batches as used. As 
mortar facing shows the roughness of the forms more readily than 



MASONRY AND REINFORCED CONCRETE 



263 



concrete does, care is required in constructing, to secure a smooth 

finish. When the forms are removed, the face may be treated either 

in the manner already described, or according to the following method 

taken from the "Proceedings" of the American Railway Engineering 

and Maintenance of Way Association : 

"After the forms are removed, any small cavities or openings in the 
concrete shall be filled with mortar, if necessary. Any ridges due to cracks or 
joints in the lumber shall be rubbed down; the entire face shall be washed with 
a thin grout of the consistency of whitewash, mixed in the proportion of 1 
part cement to 2 parts of sand. The wash shall be applied with a brush." 

319. Masonry Facing. Concrete surfaces may be finished to 

represent ashlar masonry. The process is similar to stone-dressing; 

and any of the forms of finish employed for cut stone can be used for 

concrete. Very often, when 

the surface is finished to 



^^^^^^^^^^^ ^ 



represent ashlar masonry, 
vertical and horizontal three- 
sided pieces of wood are 
fastened to the forms to 
make V-shaped depressions 
in the concrete, as shown in 
Fig. 117. 

320. Stone or Brick Facing 



Fig. 117. Masonry Facing of Concrete. 

A facing of stone or brick is 
frequently used for reinforced concrete, and is a very satisfactory 
solution of the problem of finish. The same care is required with a 
stone or brick facing as if the entire structure were stone or brick. 
The Ingalls Building at Cincinnati, Ohio, 16 stories, is veneered on the 
outside with marble to a height of three stories, and with brick and 
terra-cotta above the third story. Exclusive of the facing, the wall is 
8 inches thick. 

In constructing the Harvard University Stadium, care was 
taken, after the concrete was placed in the forms, to force the stones 
back from the face and permit the mortar to cover every stone. When 
the forms were removed, the surface was picked with a tool as 
shown in Fig. 118. A pneumatic tool has also been adopted for this 
purpose. 

The number of square feet to be picked per day, depends on the 
hardness of the concrete. If the picking is performed by hand, it is 
done by a common laborer; and he is expected to cover, on an average, 



264 



MASONRY AND REINFORCED CONCRETE 




about 50 square feet per day of ten hours. With a pneumatic tool, 
a man would cover from 400 to 500 square feet per day. 

321. Granolithic Finish. Several concrete bridges in Phila- 
delphia have been finished according to the following specifications; 
and their appearance is very satisfactory: 

"Granolithic surfacing, where required, shall be composed of 1 part 
cement, 2 parts coarse sand or gravel, and 2 parts granolithic grit, made into 

a stiff mortar. Granolithic grit shall be granite 
or trap rock, crushed to pass a j-inch sieve, and 
screened of dust. For vertical surfaces, the 
mixture shall be deposited against the face 
forms to a minimum thickness of 1 inch, by 
skilled workmen, as the placing of the concrete 
proceeds; and it thus forms a part of the body 
of the work. Care must be taken to prevent 
the occurrence of air-spaces or voids in the sur- 
face. The face shall be removed as soon as the 
concrete has sufficiently hardened; and any 
voids that may appear shall be filled with the 
mixture. The surface shall then be immediate- 
ly washed with water until the grit is exposed 
and rinsed clean, and shall be protected from 
the sun and kept moist for three days. For 
bridge-seat courses and other horizontal sur- 
faces, the granolithic mixture shall be deposited 
on the concrete to a thickness of at least H 
inches, immediately after the concrete has been 
tamped and before it has set, and shall be 
troweled to an even surface, and, after it has set sufficiently hard, shall be 
washed until the grit is exposed." . 

The success of this method depends greatly on the removal of 
the forms at the proper time. In general the washing is done the day 
following that on which the concrete was deposited. The fresh 
concrete is scrubbed with an ordinary scrubbing-brush, removing the 
film, the impressions of the forms, and exposing the sand and stone 
of the concrete. If this is done at the right time — that is, when the 
material is at the proper degree of hardness — merely a few rubs of an 
ordinary house scrubbing-brush, with a free flow of water to cut and 
to rinse clean, constitutes all. the work and apparatus required. The 
cost of scrubbing is small if done at the right time. A laborer will 
wash 100 square feet in an hour; but if that same area is permitted to 
get hard, it may require two men a day with wire brushes to secure the 
desired results. The practicability of removing the forms at the 
proper time for such treatment, depends upon the character of the 




O 



Fig. 118. Pick for Facing 
Concrete. 



MASONRY AND REINFORCED CONCRETE 



265 



structure and the conditions under which the work must be done. 
This method is applicable to vertical walls, but it would not be 
applicable to the soffit of an arch. (See Fig. 119.) 

322. The Acid Treatment. This treatment consists in washing 
the surface of the concrete with diluted acid, then with an alkaline 
solution. The diluted acid is applied first, to remove the cement and 



























Aggregate xg-Inch White Pebbles. Aggregate g-Ineh Screened Stone. 

Fig. 119. Quimby's Finish on Concrete Surfaces. Reproduced at actual size, ' 

expose the sand and stone; the alkaline solution is then applied to 
remove all of the free acid ; and finally the surface is washed with clear 
water. The treatment may be applied at any time after the forms 
are removed. It is simple and effective. Limestone cannot be used 
in the concrete for any surfaces that are to have this treatment, as the 
limestone would be affected by the acid. This process has been 
used very successfully. It is said to be patented. 

323. Dry Mortar Finish. The dry mortar method consists 
of a dry, rich mixture, with finely crushed stone. The concrete is 
usually composed of 1 part cement, 3 parts sand, and 3 parts crushed 
stone known at the J-inch size, and mixed dry so that no mortar will 



266 MASONRY AND REINFORCED CONCRETE 

flush to the surface when well rammed in the forms. When placed, 
the concrete is not spaded next to the forms; and being dry, there is 
no smooth mortar surface, but there should be an even-grained, 
rough surface. With the dry mixture, the imprint of joints of the 
forms is hardly noticed, and the grain of the wood is not seen at 
all. This style of finish has been extensively used in the South Park 
system of Chicago, and there has been no efflorescence apparent on 
the surface, which is explained by "the dryness of the mix and the 
porosity of the surf ace. " 

324. Cast Slab Veneer. Cast concrete slab veneer can be made 
of any desired thickness or size. It is set in place like stone veneer, 
with the remainder of the concrete forming 
the backing. It is usually cast in wooden 
moulds, face down. A layer of mortar, 1 
part cement, 1 part sand, and 2 or 3 parts 
fine stone or coarse sand, is placed in the 
mould to a depth of about 1 inch, and then 
, the mould is filled up with a 1:2:4 concrete. 
Any steel reinforcement that is desired may 
be placed in the concrete. Usually, cast con- 
crete slab veneer is cheaper than concrete 
facing cast in place, and a better surface 
finish is secured. 

325. Mouldings and Ornamental Shapes. 
Concrete is now in demand in ornamental 
shapes for buildings and bridges. They may- 
be either constructed in place, or moulded 
in sections and placed the same as cut stone. 
Plain cornices or panels are usually con- 
structed in place, and complicated mould- 
ing or balusters (Fig 120) are usually made 

Fig. 120. Balustrade. ,. i , i • , 

in sections and erected in separate pieces. 
The moulds may be constructed of wood, metal, or plaster of 
Paris, or moulded in sand. The operation of casting concrete in 
sand is similar to that of casting iron. The pattern is made of wood * 
the exact size required. It is then moulded in flasks exactly as done 
in casting iron. The ingredients for concrete consist of cement and 
sand or fine crushed stone; the mixture, with a consistence about 




MASONRY AND REINFORCED CONCRETE 



267 



that of cream, is poured into the mould with the aid of a funnel and a 
T-pipe. Generally the casting is left in the sand for three or four 
days, and, after being taken out of the sand, should harden in the air 
a week or ten days before being placed. Balusters are very often 
made in this manner. 

326. Colors for Concrete Finish. Coloring matter has not 
been used very extensively in concrete work, except in ornamental 
work. It has not been very definitely determined what coloring 
matters are detrimental to concrete. Lampblack (boneblack) has 
been used more extensively than any other coloring matter. It gives 
different shades of gray, depending on the amount used. Common 
lampblack and Venetian red should not be used, as they are apt to 
run or fade. Dry mineral colors, mixed in proportions of two to ten 
per cent of the cement, give shades approaching the color used. Red 
lead should never be used ; even one per cent is injurious to the con- 
crete. Variations in the color of cement and character of the sand 
used will affect the results obtained in using coloring matter. 

COLORED MORTARS 

Colors Given to Portland Cement Mortars Containing Two Parts 

River Sand to One Part Cement 



Dry 


Weight of Dry Coloring Matter to 100 Lbs. of Cement 


Cost of 


Material 
Used 


i Pound 


1 Pound 


2 Pounds 


4 Pounds 


Matter per 
Pound 


Lampblack 


Light Slate 


Light Gray- 


Blue Gray 


Dark Blue 

Slate 


15 cents 


Prussian 
Blue 


Light Green 
Slate 


Light Blue 

Slate 


Blue Slate 


Bright Blue 
Slate 


50 " 


Ultramarine 




Light Blue 
Slate 


Blue Slate 


Bright Blue 
Slate 


20 " 


Blue 






Yellow 


Light Green 






Light Buff 


3 


Ocher 








Burnt 
Umber 


Light Pink- 
ish Slate 


Pinkish 
Slate * 


Dull Laven- 
der Pink 


Chocolate 


10 " 


Venetian 
Red 


Slate, Pink 
Tinge 


Bright Pink- 
ish Slate 


Light Dull 
Pink 


Dull Pink 


2* " 


Red Iron 
Ore 


Pinkish 
Slate 


Dull Pink 


Tcrra-Cotta 


Light Brick 
Red 


2\ " 



The above table is taken from Sabin's "Cement and Concrete." 

327. Painting Concrete Surface. Special paints are made for 
painting concrete surfaces. Ordinary paints, as a general rule, are not 



26S MASONRY AND REINFORCED CONCRETE 

satisfactory. Before the paint is applied, the surface of the wall 
should be washed with dilute sulphuric acid, 1 part acid to 100 parts 
water. 

328. Finish for Floors. Floors in manufacturing buildings are 
often finished with a 1-inch coat of cement and sand, which is usually 
mixed in the proportions of 1 part cement to 1 part sand, or 1 part 
cement to 2 parts sand. This finishing coat must be put on before 
the concrete base sets, or it will break up and shell off, unless it is made 
very thick, 1J to 2 inches. A more satisfactory method of finishing 
such floors is to put 2 inches of cinder concrete on the concrete base, 
and then put the finishing coat on the cinder concrete. The finish 
coat and cinder concrete bond together, making a thickness of three 
inches. The cinder concrete may consist of a mixture of 1 part 
cement, 2 parts sand, and 6 parts cinders, and may be put down at 
any time; that is, this method of finishing a floor can be used as 
satisfactorily on an old concrete floor as on one just constructed. 

In office buildings, and generally in factory buildings, a wooden 
floor is laid over the concrete. Wooden stringers are first laid on 
the concrete, about lh to 2 feet apart. The stringers are 2 inches 
thick and 3 inches wide on top, with sloping edges. The space 




Fig. 121. Cinder Fill between Stringers. 

between the stringers is filled with cinder concrete, as shown in Fig. 
121, usually mixed 1:4:8. When the concrete has set, the flooring 
is nailed to the stringers. 

329. Efflorescence. The white deposit found on the surface 
of concrete, brick, and stone masonry is called efflorescence. It is 
caused by the leaching of certain lime compounds, which are deposited 
on the surface by the evaporation of the water. This is believed to 
be due primarily to the variation in the amount of water used in 
mixing the mortar. An excess of water will cause a segregation of 
the coarse and fine materials, resulting in a difference of color. In a 
very wet mixture, more lime will be set free from the cement and 



MASONRY AND REINFORCED CONCRETE 269 

brought to the surface. When great care is used as to the amount of 
water, and care is taken to prevent the separation of the stone from 
the mortar when deposited, the concrete will present a fairly uni- 
form color when the forms are removed. There is greater danger 
of the efflorescence at joints than at any other point, unless special 
care is taken. If the work is to be continued within 24 hours, and 
care is taken to scrape and remove the laitance, and then, before 
the next layer is deposited, the scraped surface is coated with a thin 
cement mortar, the joint should be impervious to moisture, and no 
trouble with efflorescence should be experienced. 

A very successful method of removing efflorescence from a con- 
crete surface, consists in applying a wash of diluted hydrochloric 
acid. The wash consists of 1 part acid to 5 parts water, and is 
applied with scrubbing brushes. Water is kept constantly played on 
the work, by means of a hose, to prevent the penetration of the acid. 
The cleaning is very satisfactory, and for plain surfaces costs about 
20 cents per square yard. 

330. Laitance. Laitance is whitish, spongy material that is 
washed out of the concrete when it is deposited in water. Before 
settling on the concrete, it gives the water a milky appearance. It 
is a semi-fluid mass, composed of a very fine, flocculent matter in the 
cement; generally contains hydrate of lime; stays in ,a semi-fluid 
state for a long time; and acquires very little hardness at its best. 
Laitance interferes with the bonding of the layers of concrete, and 
should always be thoroughly cleaned from the surface before another 
layer of concrete is placed. 

MACHINERY FOR CONCRETE WORK 

331. Concrete Plant. No general rule can be given for laying 
out a plant for concrete work. Every job is generally a problem by 
itself, and usually requires a careful analysis to secure the most 
economical results. Since it is much easier and cheaper to handle the 
cement, sand, and stone before they are mixed, the mixing should 
be done as near the point of installation as possible. All facilities for 
handling these materials, charging the mixer, and distributing the 
concrete after it is mixed, must be secured and maintained. The 
charging and distributing are often done by wheelbarrows or carts; 
and economy of operation depends largely upon system and regu- 



270 MASONRY AND REINFORCED CONCRETE 

larity of operation. Simple cycles of operations, the maintenance 

of proper runways, together with clock-like regularity, are necessary 

for economy. To shorten the distance of wheeling the concrete, it is 

very often found, on large buildings, that it is more economical to 

have two medium-sized plants located some distance apart, than 

to have one large plant. In city work, where it is usually impossible 

to locate the hoist outside of the building, it is constructed in the 

elevator shaft or light well. In purchasing a new plant, care must 

be exercised in selecting machinery that will not only be satisfactory 

for the first job, but that will fulfil the general needs of the purchaser x^ 

on other work. All parts of the plant, as well as all parts of any one 

machine, should be easily duplicated from stock, so that there will 

not be any great delay from any breakdown or worn-out parts. 

The design of a plant for handling the material and concrete, 
and the selection of a mixer, depend upon local conditions, the 
amount of concrete to be mixed per day, and the total amount re- 
quired on the contract. It is very evident that on large jobs it pays 
to invest a large sum in machinery to reduce the number of men and 
horses; but if not over 50 cubic yards are to be deposited per day, the 
cost of the machinery is a big item, and hand labor is generally 
cheaper. The interest on the plant must be charged against the 
number of cubic yards of concrete; that is, the interest on the plant 
for a year must be charged to the number of cubic yards of concrete 
laid in a year. The depreciation of the plant is found by taking the 
cost of the entire plant when new, and then appraising it after the 
contract is finished, and dividing the difference by the total cubic 
yards of concrete laid. This will give the depreciation per cubic 
yard of concrete manufactured. 

332. Concrete Mixers. The best concrete mixer is the one that 
turns out the maximum of thoroughly mixed concrete at the mini- 
mum of cost for power, interest, and maintenance. The type of 
mixer with a complicated motion gives better and quicker results than 
one with a simpler motion. There are two general classes of con- 
crete mixers — continuous mixers and batch mixers. A continuous 
mixer is one into which the materials are fed constantly, and from 
which the concrete is discharged constantly. Batch mixers are con- 
structed to receive the cement with its proportionate amount of sand 
and stone, all at one charge; and, when mixed, it is discharged in a 



MASONRY AND REINFORCED CONCRETE 



271 



mass. No very distinct line can be drawn between these two classes, 
for many of these mixers are adapted to either continuous or batch 
mixing. Generally, batch mixers are preferred, as it is a very diffi- 
cult matter to feed the 
mixers uniformly un- 
less the materials 
are mechanically 
measured. 

Continuous mixers 
usually consist of a 
long screw or pug mill, 
that pushes the ma- 
terials along a drum 
until they are dis- 
charged in a continu- 
ous stream of concrete. 
Where the mixers are 
fed with automatic 
measuring devices, the 
concrete is not regular, 
as there is no recipro- 
cating motion of the 
materials. Tn a paper 
recently read before 
the Association of 
American Portland 
Cement Manufac- 
turers, S. B. Newberry 
says: 

" For the preparation 
of concrete for blocks in 
which thorough mixing 
and use of an exact and Fig " m POTtaWe Gravit y Mixer - 

uniform proportion of water are necessary, continuous mixing machines are 
unsuitable ; and batch mixers, in which a measured batch of the material is 
mixed the required time, and then discharged, are the only type which will 
be found effective." 

There are three general types of concrete mixers : gravity mixers, 
rotary mixers, and paddle mixers. 

Gravity mixers are the. oldest type of concrete mixers. They 




272 



MASONRY AND REINFORCED CONCRETE 



require no power, the materials being mixed by striking obstructions 
which throw them together in their descent through the machine. 

Their construction is very sim- 
ple. Fig. 122 illustrates a port- 
able gravity mixer. This mixer, 
as will be seen from the figure, is 
a steel trough or chute in which 
are contained mixing members 
consisting of pins or blades. 
The mixer is portable, and re- 
quires no skilled labor to oper- 
ate it. There is nothing to get 
out of order or cause delays. 
It is adapted for both large and 
small jobs. In the former case, 
it is usually fed by measure, and 
by this method will produce con- 
crete as fast as the materials can be fed to their respective bins 
and the mixed concrete can be taken from the discharge end of the 




Fig. 123. Operation of Portable Gravity 
Mixer. 




■(■■ 







Fig. 121. Rotary Mixer with Cubical Box. 




MASONRY AND REINFORCED CONCRETE 273 




Fig. 125. Rotary Mixer Mounted on Frame. 




Fig. 126. Cross-Section of Drum of Rotary Mixer (front half cut away), 
Showing Blades and Lining. 



274 



MASONRY AND REINFORCED CONCRETE 



mixer. On very small jobs, the best way to operate is to measure 
the batch in layers of stone, sand, and cement respectively, and feed 
to the mixer by men with shovels. 

There are two spray pipes placed on the mixer : for feeding 
by hand, one spray only would be used; the other spray is intended 
for use only when operating with the measure and feeder, and a 

large amount of 
water is required. 
These sprays are 
operated by han- 
dles which control 
two gate- valves 
and regulate the 
quantity of water 
flowing from the 
spray pipes. 

These mixers 
are made in two 
styles, sectional 
and non-sectional. 
The sectional can 
be made either 4, 

Fig. 137. Ransome Batch Mixer. (^ or g f ee t long. 

The non-sectional are in one length of 6, 8, or 10 feet. Both are 
constructed of ^-inch steel. To operate this mixer, the materials 
must be raised to a platform, as shown in Fig. 123. 

Rotary mixers, Fig. 124, generally consist of a cubical box made 
of steel and mounted on a wooden frame. This steel box is supported 
by a hollow shaft through two diagonally opposite corners, and the 
water is supplied through openings in the hollow shaft. Materials 
are dropped in at the side of the mixer, through a hinged door. The 
machine is then revolved several times, usually about 15 times; the 
door is opened; and the concrete is dumped out into carts or cars. 
There are no paddles or blades of any kind inside the box to assist 
in the mixing. This mixer is not expensive itself, but the erection 
of the frame and the hoisting of the stone and sand often render it 
less economical than some of the more expensive devices. 

Rotating mixers which contain reflectors or blades, Fig. 125, 




MASONRY AND REINFORCED- CONCRETE 



275 



are usually mounted on a suitable frame by the manufacturers. The 
rotating of the drum tumbles the material, and it is thrown against 
the mixing blades, which cut it and throw it from side to side. Many 
of these machines can be filled and dumped while running, either 
by tilting or by their chutes. Fig. 125 illustrates the Smith mixer, 
and Fig. 126 gives a sectional view of the drum, and shows the 
arrangement of the blades. This mixer is furnished on skids with 




Fig. 128. McKelvey Batch Mixer. 

driving pulley. The concrete is discharged by tilting the drum, which 
is done by power. 

Fig. 127 represents a Ransome mixer, which is a batch mixer. 
The concrete is discharged after it is mixed, without tilting the body 
of the mixer. It revolves continuously even while the concrete is 
being discharged. Riveted to the inside of the drum are a number of 
steel scoops or blades. These scoops pick up the material in the 
bottom of the mixer, and, as the mixer revolves, carry the material 
upward until it slides out of the scoops, which therefore assist m 
mixing the materials. 

Fig. 128 represents a McKelvey batch mixer. In this mixer, the 
lever on the drum operates the discharge. The drum is fed and dis- 
charged while in motion, and does not change its direction or its 



276 



MASONRY AND REINFORCED CONCRETE 



position in either feeding or discharging. The inside of the drum is 
provided with blades to assist in the mixing of the concrete. 

Paddle mixers may be either continuous or of the batch type. 
Mixing paddles, on two shafts, revolve in opposite directions, and the 
concrete falls through a trap door in the bottom of the machine. In 
the continuous type the materials should be put in at the upper end 
so as to be partially mixed dry. The water is supplied near the 
middle of the mixer. Fig. 129 represents a type of the paddle mixer. 

333. Automatic Measures for Concrete Materials. Mechanical 
measuring machines for concrete materials have not been very ex- 



uv 




Fig. 129. Paddle Mixer. 

tensively developed. One difficulty is that they require the constant 
attention of an attendant, unless the materials are perfectly uniform. 
If the machine is adjusted for sand with a certain percentage of 
moisture, and then is suddenly supplied with sand having greater 
or less, moisture, the adjustment must be changed or the mixture 
will not be uniform. If the attendant does not watch the condition 
of the materials very closely, the proportions of the ingredients will 
vary greatly from what they should. 

The Trump measuring device, shown in Fig. 130, consists of a 
horizontal revolving table on which rests the material to be measured, 
and a stationary knife set above the table and pivoted on a vertical 
shaft outside the circumference. The knife can be adjusted to extend 
a proper distance into the material, and to peel off, at each revolution 



MASONRY AND REINFORCED CONCRETE 



277 



of the table, a certain amount, which falls into the chute. The 
material peeled off is replaced from the supply contained in a bottom- 
less storage cylinder somewhat smaller in diameter than the table and 
revolving with it. The depth of the cut of the knife is adjusted by 
swinging the knife around on its pivot so that it extends a greater or 




Fig. 130. Trump Measuring Device. 



less distance into the material. The swing is controlled by a screw 
attached to an arm cast as part of the knife. A micrometer scale, 
with pointer, indicates the position of the knife. When it is desired 
to measure off and mix three materials, the machines are made with 
three tables set one above the other and mounted on the same spindle 
so that they revolve together. Each table has its own storage 
cylinder above it, the cylinders being placed one within the other, as 
shown in Fig. 131. 



278 



MASONRY AND REINFORCED CONCRETE 



334. Source of Power. In each case the source of power for 
operating the mixer, conveyors, hoists, derricks, or cableways must be 
considered. If it is possible to run the machinery by electricity, it 
is generally economical to do so. But this will depend a great deal 




Fig. 131. Interior View of Trump Concrete Mixer. 

upon the local price of electricity. When all the machinery can be 
supplied with steam from one centrally located boiler, this arrange- 
ment will be found perhaps more efficient. 

In the construction of some reinforced-concrete buildings, a part 
of the machinery was operated by steam and part by electricity. In 
constructing the Ingalls Building, Cincinnati, the machinery was 



MASONRY AND REINFORCED CONCRETE 



279 



operated by a gas engine, electric motor, and a steam engine. The 

mixer was generally run by a motor; but by shifting the belt, it could 

be run by the gas engine. The hoisting was done by a 20-horse- 

power Lidgerwood engine. This engine was also connected up to a 

boom derrick, to hoist lumber and steel. The practice of operating 

the machinery of one plant by power from different sources, is to be 

questioned; but the practice of operating the 

mixer by steam and the hoist by electricity 

seems to be very common in the construction 

of buildings. A contractor, before purchasing 

machinery for concrete work, should carefully 

investigate the different sources of power for 

operating the machinery, not forgetting to 

consider the local conditions as well as general 

conditions. 

335. Power for Mixing Concrete. A ver- 
tical steam engine is generally used to operate 
the mixer. 'The smaller sizes of engines and 
mixers are mounted on the same frame; but 
on account of the weight, it is necessary to 
mount the larger sizes on separate frames. 
Fig. 132 shows a Ransomedisc crank vertical 
engine, and Table XIX is taken from a Ran- 
some catalogue on concrete machinery. These 
engines are well-built, heavy in construction, 
and will stand hard work and high speed. 

336. Gasoline Engines. Gasoline engines are used to some 
extent to operate concrete mixers. Their use so far has been limited 
chiefly to portable plants such as are used for street work. The fuel 
for the gasoline engine is much easier moved from place to place 
than the fuel for a steam engine. Another advantage that the gaso- 
line engine has over the steam engine is that it does not require the 
constant attention of an engineer. 

There are two types of engines — the horizontal and the vertical. 
The vertical engines occupy much less floor space for a given horse- 
power than the horizontal. While each type has its advantages and 
disadvantages, there does not really appear to be any very great 
advantage fo one type over the other. Both types of engines are 




Fig. 133. Ransome Disc 
Crank Vertical Engine. 



280 



MASONRY AND REINFORCED CONCRETE 



TABLE XIX 
Dimensions for Ransome Engines 



No. of Mixer 


1 


2 


3 


4 


Size of Batch 


10 CU: ft. 


20 cu. ft, 


30 cu. ft. 


40 cu. ft. 


Capacity per hr. 
(Cu. yds.) 


10 


20 


30 


40 


Horse-Power 
Required^ 


'Engine 
Rated 

Boiler 
Rated 


6 bv6 

7h! p. 

30 by 72 
10 h. p. 


7 by 7 
10 h. p. 

36 by 78 
15 h. p. 


8 by 8 
14 h p. 

36 by 96 
20 h. p. 


9 by 9 
20 h. p. 

42 by 102 
30 h. p. 


Speed of Drum 

(Rev. per Min.) 


16 


15 


14J 


14 


Speed of Driving Shaft 
(Rev. per Min.) 


116 


122 


94 


99 



what is commonly known as four-cycle engines. In the operation of 
a 4-cycle engine, four strokes of the piston are required to draw in a 

charge of fuel, compress and ignite 
it, and discharge the exhaust 
gases. Fig. 133 shows a vertical 
gasoline engine made by the In- 
ternational Harvester Company. 
The quantity of gasoline con- 
sumed in ten hours, on an average, 
is about one gallon for each rated 
horse-power for any given size of 
engine. At 15 cents per gallon 
for gasoline, the hourly expense 
per horse-power will be 1.5 cents. 
337. Hoisting Concrete. When 
the concrete requires hoisting, it 
is done sometimes by the same 
engine that is used in mixing the 
concrete. It is generally con- 

Vertical Gasoline Engine. sidered ^^ practice on large 

buildings to have a separate unit to do the hoisting. If it is possible 
to use a standard hoist, it is usually economical to do so. These 
hoists are equipped with automatic dump buckets. 




MASONRY AND REINFORCED CONCRETE 



281 



Fig. 134 shows a standard double-cylinder, double-friction-drum 
hoisting engine of the Lambert type. This type of engine is designed 
to fulfil the requirements of a general contractor for all classes of 
derrick work and hoisting. Steam can be applied by a single boiler, 
or from a boiler that supplies various engines with steam. The 
double friction drums are independent of each other; therefore one 




Fig. 134. "Lambert" Hoisting Engine. 

or two derricks can be handled at the same time, if desired. This 
hoist is fitted with ratchets and pawls, and winch-heads attached to 
the end of each drum-shaft. The winch-heads can be used for any 
hoisting or hauling desired, independent of the drums. These engines 
are also geared with reversible link motion. 

338. Friction Crab Hoist. A friction crab hoist of the Ransome 
type is illustrated in Fig. 135. The same engine that drives the 
mixer can be used to operate the crab hoist. By means of a sprocket- 
wheel and chain, this crab hoist can be geared to any engine, and, 
when so geared, is ready for hoisting purposes. The hoisting drum 
is controlled by one lever. This hoist can be run by an electric 
motor, if desired. On account of the low price, the friction crab has 
found much favor with contractors. 

339. Electric Motors. Very often the cycle of operation of a 
hoist is of an intermittent character. The power required is at a 



282 



MASONRY AND REINFORCED CONCRETE 



TABLE XX 
Tables of Sizes of the Lambert Hoisting Engines 



Horse- 
Power 

Usually 
Rated 



10 
14 
20 
25 
30 
35 
40 



Dimensions of 
Cylinders 


Dimensions of 
Drums 


Diameter 

(Inches) 


Stroke 
(Inches) 


Diameter 
(Inches) 


Length 
between 
Flanges 
(Inches) 

16 


5* 


8 


12 


6* 


8 


12 


16 


7 


10 


14 


18 


7| 


10 


14 


24 


8i 


10 


14 


24 


9 


10 


14 


24 


9£ 


10 


16 


23 



Weight 

Hoisted, 

Single Line 



2,500 
3,000 
5,000 
6,500 
8,000 
9,000 
10,000 



Suitable 

Weight for 

Pile- Driving 

Hammer 

for 

Quick Work 



1,600 
2,000 
3,000 
4,000 
5,000 
5,000 
6,000 



maximum only a part of the time, even though the hoist may be 
operated practically continuously. From an economical point of 
view, these conditions give the electric motor-driven hoist special 
advantages, in that the electric hoist should always be ready, but 
using power only when in actual operation and then only in propor- 
tion to the load handled. The ease with which a motor is moved, 
and the simplicity of the connection to the service supply, re- 
quiring only two wires to be connected, are also in favor of the 
electric motor. 

Fig. 136 shows a motor made by the Westinghouse Electric & 
Manufacturing Company, which is designed for the operation of 
cranes, hoists, or for intermittent service in which heavy starting 
torques and a wide speed variation are required. The frames are 
enclosed to guard against dirt and moisture, but are so designed that 
the working parts may be exposed for inspection or adjustment 
without dismantling. These motors are series- wound, and are 
designed for operating on direct-current circuits. The motor frames 
are of cast steel, nearly square in section and very compact. The 
frame is built in two parts, and so divided that the upper half of the 
field can be removed without disturbing the gear or shaft, making it 
easy to take out a pole-piece and field-coils, or to remove the armature. 
Fig. 137 shows the controller for this type of motor. These con- 
trollers, when used for crane service, may be placed directly in the 
crane cage and operated by hand, or mounted on the resistance frames 
outside the cage, and operated by bell cranks and levers, so that the 



MASONRY AND REINFORCED CONCRETE 



283 



attendant may stand closer to the operating handles and away from 
the contacts and resistance. 

Polyphase induction motors are being used to some extent for 
general hoisting and derrick work. These motors may be of the 
two-phase or three-phase type; but the latter are slightly more 
efficient. These motors are provided with resistances in the rotor 






Fig. 135. Ransome Friction 
Crab Hoist. 



Fig. 136. Motor with Fields Parted. 
For operation of cranes, hoists, etc. 



circuit, and with external contacts for varying the same. Two 
capacities of resistance can be furnished: (a) Intermittent service, 
zero to full load; and (b) Intermittent service, zero to half- 
speed; and continuous service, half-speed to full speed. The 
controllers are of the drum type, similar to those used on street- 
cars. 

340. Hoisting Lumber and Steel. In constructing large rein- 
forced-concrete buildings, usually a separate hoist is used to hoist 
the steel and lumber for the forms. This hoist may be equipped 
with either an electric motor or an engine, depending upon the general 



2S4 



MASONRY AND REINFORCED CONCRETE 




Fig. 137. 



Regulating and Reversing Controller 
for Motor of Fig. 136. 



arrangement of the plant. These hoists 
are usually of the single-drum type. 

341. Hoisting Buckets. In build- 
ing construction, concrete is usually 
hoisted in automatic dumping buckets. 
The bucket is designed to slide up and 
down a light framework of timber, as 
shown in Fig. 138, and to dump auto- 
matically when it reaches the proper 
place to dump. The dumping of the 
buckets is accomplished by the bucket 
pitching forward at the point where 
the front guide in the hoisting tower 
is cut off. The bucket rights itself 
again automatically as soon as it be- 
gins to descend. These buckets are 
often used for hoisting sand and stone 
as well as concrete. The capacity of 
these buckets varies from 10 cubic feet 
to 40 cubic feet. Fig. 139 shows a 
Ransome bucket which has been satis- 
factorily used for this purpose. 

342. Charging Mixers. The mixers 
are usually charged by means of wheel- 
barrows, although other means are 




Elevation 




Fig. 138. Detail of Hoisting Tower, 
■with Automatic Dumping 
Bucket. 



MASONRY AND REINFORCED CONCRETE 



285 



sometimes used. Fig. 140 shows the type of wheelbarrow generally 
used for this work. The capaeity varies from 2 cubic feet to 4 cubic 
feet, the latter size being generally used, as with good runways, a 
man can handle four cubic feet of stone or sand in a well-constructed 
wheelbarrow. 

In ordinary massive concrete construction, as foundations, piers, 
etc., where it is not necessary to 
hoist the concrete after it is mixed, 
the mixer is usually elevated so that 
the concrete can be discharged 
directly into wheelbarrows, carts, 
cars, or a chute from which the 
wheelbarrows or carts are filled. It 
is much better to discharge the 
concrete into a receiving chute than 
to discharge it directly into the 
conveyor. The chute can be emp- 
tied while the mixer is being charged 
and rotated; while, if the concrete 
is discharged directly into wheel- 
barrows or carts, there must be sufficient wheelbarrows or carts 
waiting to receive the discharge, or the man charging the mixer will 
be idle while the mixer is being discharged. A greater objection is 
that if the man in charge of the mixer finds that the charging men or 




Fig. 139. "Ransome" Concrete 
Hoist-Bucket. 




Fig. 140. "Sterling" Contractor's Wheelbarrow. 

conveying men are waiting, he is very apt to discharge the concrete 
before it is thoroughly mixed, in an effort to keep all the men busy. 
A platform is built at the elevation of the top of the hopper, through 
which the materials are fed to the mixer, Fig. 141. This is a rather 



286 



MASONRY AND REINFORCED CONCRETE 



expensive operation for mixing concrete, and should always be avoided 
when possible. 

Fig. 142 shows a charging elevator devised by the McKelvey 
Machinery Company. The bucket is raised and lowered by the same 
engine by which the concrete is mixed, and operated by the same man. 
The capacity of the charging bucket is the same as that of the mixer. 

In Fig. 143 is shown an automatic loading bucket which has been 
devised by the Koehring Machine Company for charging the mixers 
made by them. The bucket is operated by a friction clutch, and is 




Fig. 141. Concrete Mixer Erected. 



provided with an automatic stop. In using either make of these 
charging buckets, it is necessary to use wheelbarrows to charge the 
buckets, unless the materials are close to the mixer. 

343. Transporting Concrete. Concrete is usually transported 
by wheelbarrows, carts, cars, or derricks, although other means are 
frequently used. It is essential, in handling or transporting con- 
crete, that care be taken to prevent the separation of the stone from 
the mortar. With a wet mixture, there is not so much danger of the 
stone separating. Owing to the difference in the time of setting of 
Portland cement and Natural cement, the former can be conveyed 
much farther and with less danger of the initial setting taking place 
before the concrete is deposited. When concrete is mixed by hand, 
wheelbarrows are generally used to transport the concrete; and tbev 



MASONRY AND REINFORCED CONCRETE 



287 



are very often used also for transporting machine-mixed concrete. 
The wheelbarrows used are of the same type as shown in Fig. 140. 
About two cubic feet of wet concrete is the average load for a man to 
handle in a wheelbarrow. 

Fig. 144 shows a cart of the Koehring make, for transporting 
concrete. The 
capacity of these 
carts is six cubic 
feet. One man can 
push or pull these 
carts over a plank 
runway. The run- 
way consists of two 
planks, each 8 to 
10 inches wide, fast- 
ened together with 
1-inch by 6-inch 
cross-piece's, and 
made in sections so 
that they can be 
easily handled by 
two men. 

When it is neces- 
sary to convey con- 
crete a longer dis- 
tance than it is 
economical to do so 
by wheelbarrows or 
carts, a dumping 
car run on a track 
is often used. Fig. 
145 shows a steel 
car for this purpose. The capacity of these cars is from 10 cubic feet 
to 40 cubic feet, and the track gauge is from 18 inches to 36 inches. 
Both end and side dumping cars are made. 

If a large amount of concrete is to be deposited near where it is 
mixed, derricks are frequently used to convey the concrete. A com- 




X 



Fig. 142. "McKelvey" Chai'ging Bucket Discharging Batch 
into Mixer Operated by Same Power. 



288 



MASONRY AND REINFORCED CONCRETE 



bination of car and derrick work is easily made by using flat cars with 
derrick buckets. 

344. Boilers. Upright tubular boilers are generally used to 

supply steam for 




Automatic Loading Bucket. 



ened to the same frame as the hoisting engine, 
cannot be used for the larger sizes of mixers 
are too heavy to be 



concrete mixers and 
hoists operated by 
steam engines, when 
they are isolated. 
For the smaller 
sizes of mixers, the 
boilers are on the 
same frame as the 
engine and mixer. 
Fig. 128 shows a 
McKelvey mixer, 
engine, and boiler 
mounted on the 
same frame. In a 
similar mariner the 
boiler is often fast- 
This arrangement 
md hoists, as they 



conven- 



handled 
iently. 

When it is pos- 
sible, the mixer and 
hoists should be 
supplied with steam 
from one centrally 
located boiler. A 
portable boiler is 
then generally used. 

345. Wood= 
working Plant. A 
portable wood- 
working plant can 
very often be used to advantage in shaping the lumber for the forms 




Fig. 144. "Koehring" Concrete Cart. 



MASONRY AND REINFORCED CONCRETE 



289 



when a large building is to be erected. The plant can be set near the 
site of the building to be erected, and the woodworking done there. 
The machinery for such a plant should consist of a planer adapted 
for surfacing lumber on three sides, a rip saw, a crosscut circular 
saw ; and in some cases a band saw can be used to advantage. Usually, 
the difference in cost between surfaced and unsurfaced lumber is so 
small that the lumber could not be surfaced in a plant of this kind, 
for the difference in cost; but perhaps it would be more uniform in 
thickness. In such a 
plant the rip saw and the 
crosscut saw would be 
found to be the most 
useful; and if reasonable 
care is taken, this ma- 
chinery will soon pay for 
itself. It is often diffi- 
cult to get work done 
at a planing mill when it 
is wanted ; and if a con- 
tractor has his own wood- 
working machinery, he 
will be independent of 
any planing mill. A 
plant of this kind can be operated by a s*eam or gasoline engine or 
an electric motor. 

346. Plant for Ten=Story Building. The plant used by Cramp 
& Company in constructing a reinforced-concrete building for the 
Boyertown Burial Casket Company, Philadelphia, will be described, 
to show the arrangement of the plant rather than the make of the 
machinery used. The building is 80 feet by 120 feet, and is ten 
stories high; also, there is a mezzanine floor between the first and 
second floors. This building is structurally of reinforced concrete, 
except that the interior columns in the lower floors were constructed 
of angles and plates and fireproofed with concrete. The power plant 
for the building is to be located at a level of about seven feet below 
the basement floor. The hoisting shaft is built in the elevator shaft 
located in the rear of the building. The hoisting tower is constructed 
of four 4 by 4-inch corner-posts, and well braced with 2 by 6-inch 




Fig. 145. Steel Body End Dump Car. 



290 



MASONRY AND REINFORCED CONCRETE 



plank. Two guides are placed on opposite sides; also one on the 
front, Fig. 146. The front guide was made in lengths equal to the 
height of different floors of the building. Fig. 146 shows the location 
of all the machinery, all of which is of the Ransome make. The con- 
crete was discharged directly-from the mixer into the bucket, which 



Basement 
Floor 

V////// 



Platfor m 




Floor 



Y// ///^////////^//7///^///////7Z^ 

Elevation 



Exterior Wall 




wv'ncn Head 
Engine 



Fig. 146. Concrete Plant for Ten-Story Building. 

rested at the bottom of the elevator shaft. At the elevation where it 
was desirable to dump the concrete, the front slide was taken out, 
and the concrete was dumped automatically by the bucket tipping 
forward. The bucket rights itself as soon as it begins to descend. 

The capacity of the mixer and hoisting bucket per batch, was 20 



MASONRY AND REINFORCED CONCRETE 291 

cubic feet. A 9 by 9-inch, 20-horse-power vertical engine was used 
to mix and hoist the concrete, steel, structural steel for columns, and 
lumber for the forms. A 30-horse-power boiler was used to supply 
the steam, which was located several feet from the engine, and is not 
shown in the plan view of the plant. A Ransome friction crab hoist 
was used to hoist the concrete, and was connected to the engine 
by a sprocket-wheel and chain. The steel and lumber were hoisted 
by means of a rope, wrapped three or four times around a 
winch-head which was on the same shaft as the mixer. The rope 
extended vertically up from the pulley, through a small hole in the 
floors, to a small pulley at the height required to hoist the lumber or 
steel; and then it extended horizontally to another pulley at the 
place where the material was to be hoisted. The rope descends over 
the pulley to the ground. A man was stationed at the engine to 
operate the rope. There were two rope-haulages operated from the 
pulley on the engine shaft, one being used at a time. On being given 
the signal, the operator wrapped the rope around the winch-head 
three or four times, kept it in place, and took care of the rope that 
ran off the pulley as material was being hoisted. 

Wheelbarrows were used in charging the mixer, and hand-carts 
were used in distributing the concrete. The runways were made by 
securely fastening two 2 by 10-inch planks together in sections of 
12 feet to 16 feet, which were handled by two men. By keeping the 
runway in good condition, two men were generally able to distribute 
the concrete, except on the lower floors, and when it was to be trans- 
ported the full length of the building. The capacity of the carts was 
6 cubic feet each. Concrete for the ninth floor was hoisted and 
placed at the rate of 15 cubic yards per hour. 

347. Plant for the Locust Realty Company Building. The plant 
used for constructing a five-story reinforced-concrete building, 117 
feet by 200 feet, for the Locust Realty Company, by Moore & Com- 
pany, Inc., is a good example of a centrally located plant. Near the 
center ot *he building is an elevator shaft, in which was constructed 
the framework for hoisting the concrete. Fig. 147 shows the arrange- 
ment of the plant, which is located in the basement and near the 
center of the building. The mixer is located so that the concrete can 
be dumped directly into the hoisting bucket. The chute for re- 
ceiving the materials being about 18 inches above the basement floor, 



292 



MASONRY AND REINFORCED CONCRETE 



it was therefore necessary to wheel the materials up an incline. An 
excavation was made below the level of the basement floor for the 
hoisting bucket. The mixing was done by a steam engine located on 
the same frame as the mixer. The concrete was hoisted by a hoisting 
engine which was located about twenty feet from the shaft. A 
small hoisting engine was also used for hoisting the steel and lumber 
used for forms; as this engine was located some distance from the 
rest of the plant, it is not shown in Fig. 147. The three engines are 
supplied with steam from a portable boiler which is located as 
shown in the figure. The efficiency of this plant was shown in the 

mixing and hoisting of the con- 




Enqim 



Hopper-* 



Boiler 



Mixer J Hoistino 3 haft 



Hoisting 
Engine 



Fig. 147. 



Concrete Plant foi- Locust Realty 
Company Building. 



crete for the second floor, when 
240 cubic yards were mixed and 
hoisted in 16 hours, or at an aver- 
age rate of one cubic yard in four 
minutes. 

All materials were delivered 
at the front of the building; and 
therefore it was necessary to 
transport the cement, sand, and 
stone about 100 feet to the mixer. 
This was done by means of wheel- 
barrows especially designed and 
made for Moore & Company, Inc, 
The concrete was a 1:2:4 mix, 
The materials for a 



the capacity being four cubic feet. 

and was mixed in batches of 14 cubic feet. 

batch, therefore, consisted of 2 bags of cement, 1 wheelbarrow of 

sand, and 2 wheelbarrows of stone. 

The lumber for the forms was lj-inch plank, except the support 
and braces. Details of the forms will be given and discussed under 
the heading of "Forms." 

348. Concrete Plant for Street Work. A self-propelling mixing 
and spreading machine has been found very desirable for laying con- 
crete base for street pavements. Fig. 148 illustrates a plant of this 
kind, which has been devised by the Municipal Engineering & Con- 
tracting Company. One of these machines was very successfully 
used in Buffalo, N. Y., in 1907. 

The mixer is of the improved cube type, mounted on a heavy 



MASONRY AND REINFORCED CONCRETE 



293 



truck frame. The con- 
crete is discharged into 
a specially designed 
bucket, which receives 
the whole batch and 
travels to the rear on a 
truck which is about 25 
feet long. The head of 
the truck is supported 
by guys, and also by a 
pair of small wheels near 
the middle of the truck, 
which rest on the graded 
surface of the street. 
The truck or boom is 
pivoted at the end con- 
nected to the main truck, 
and has a horizontal 
swing of about 170 de- 
grees, so that a street 50 
feet wide is covered. An 
inclined track is also con- 
structed, on which a 
bucket is operated for 
elevating and charging 
the mixer. The bucket 
is loaded while resting 
on the ground, with the 
proper ingredients for a 
batch, from the materials 
that have been distribu- 
ted in piles along the 
street. The bucket is 
then pulled up the in- 
cline, and the contents 
dumped into the mixer. 
An automatic water- 
measuring supply tank 




294 



MASONRY AND REINFORCED CONCRETE 



mounted on the upper part of the frame insures a uniform amount 
of water for each batch mixed. The power for hoisting, mixing, and 
distributing the concrete, and propelling the machine, was furnished 
by a 16-horse-power gasoline engine of the automobile type. The 
machine can be moved backward as well as forward, and is supplied 
with complete steering gear. 

The capacity per charge of the mixer and charging and distrib- 
uting buckets used at Buffalo, was 11 cubic feet. The crew con- 
sisted of 16 men and a foreman, and they mixed and laid from 110 
to 120 cubic yards per hour. Their best record was 1,000 cubic yards 




Fig. 149. "Hercules" Cement Stone Machine. 



in an eight-hour day. The thickness of the concrete base laid was 
6 inches. 

349. Concrete Block Machines. There are two general types 
of hollow concrete block machines on the market — those with a 
vertical face and those with a horizontal face. In making blocks 
with the vertical-faced machine, the face of the block is in a vertical 
position when moulded, and is simply lifted from the machine on its 
base-plate. The horizontal-faced (or face-down) block is made with 
the face down, the face-plate forming the bottom of the mould. The 
cores are withdrawn horizontally, or the mould is turned over and the 
core is taken out vertically; the block is then ready for removal. The 
principal difference in the two types of machine, is that, if it is desired 
to put a special facing on the block, it is more convenient to do it with 
a horizontal-faced machine. With the vertical-faced machine, the 
special facing is put on by the use of a parting plate. When the part- 



MASONRY AND REINFORCED CONCRETE 



295 



ing plate is removed, the two mixtures of concrete are bonded together 
by tamping the coarser material into the facing mixture. 

Fig. 149 shows a Hercules machine. The foundation parts can 
be attached for making any length of block up to 6 feet. The illus- 
tration shows two moulds of different lengths attached. These 
machines are constructed of iron and steel, except that the pallets 
(the plates on which the blocks are taken from the machine) may be 
either wood or steel. This type of machine is the horizontal or face- 
down machine. 

Another machine of the face-down type is shown in Fig. 150. 
This machine, the Ideal, is sim- 
ple in construction and opera- 
tion; they are portable, which 
makes them convenient to oper- 
ate. In making blocks with this 
machine, the cores are removed 
by means of a lever, while the 
block is in the position in which 
it was made. The mould and 
block are then turned over, and 
the face- and end-plates are re- 
leased, and the block removed on 
the pallet. 

In Fig. 151 are shown a group 
of the various forms which may be made. The figure also illustrates 
the facility with which concrete may be utilized for ornamental as 
well as structural purposes. 

Cement Brick Machines. Fig. 152 shows a machine for making 
cement brick. Ten bricks, 2| by 3J by 8 inches, are made at 
one operation. By using a machine in which the bricks are made 
on the side, a wetter mixture of concrete can be used than if they are 
made on the edge. The concrete usually consists of a mixture of 1 
part Portland Cement and 4 parts sand. The curing of these bricks 
is the same as that for concrete blocks. In making these bricks, a 
number of wooden pallets are required, as the brick should not be 
removed from the pallet until the concrete has set. 

350. Sand Washing. It becomes necessary sometimes to wash 
dirty sand when clean sand can be secured only at a high cost, while 




Fig. 150. "Ideal" Concrete Block Machine. 



296 



MASONRY AND REINFORCED CONCRETE 



the dirty sand can be easily obtained. If only a small quantity is to 
be washed, it may be done with a hose. A trough should be built 
about 8 feet wide and 15 feet long, the bottom having a slope of 
about 19 inches in its entire length. The side should be about 8 
inches high at the lower end, and increase gradually to a height of 
about 36 inches at the upper end. In the lower end of the trough, 
should be a gate about 6 inches high, sliding in guides so that it can 
be easily removed. The sand is placed in the upper end of the 




Fig. 151. Group of Blocks Made on "Hercules" Machines. 

trough, and a stream of water is played on it. The sand and water 
flow down the trough, and the dirt passes over the gate with the 
overflow water. With a trough of the above dimensions, and a stream 
of water from a f-inch hose, three cubic yards of sand should be 
washed in an hour. 

Concrete mixers are often used for washing sand. The sand is 
dumped into the mixer in the usual manner, and the water is turned 
on. When the mixer is filled with w T ater so that it overflows at the 
discharge end, the mixer is started. By revolving the mixer, the 
water is able to separate the dirt from the sand, and it is carried off 
by the overflow of water. When the water runs clear, the washing 
is completed, and the sand is dumped in the usual way. 

When large quantities of sand are required to be washed, special 
machinery for that purpose should be employed. 



MASONRY AND REINFORCED CONCRETE 297 

FORMS 

351. General Requirements. In actual construction work, the 
cost of forms is a large item of expense and offers the best field for the 
exercise of ingenuity. For economical work, the design should consist 
of a repetition of identical units; and the forms should be so devised 
that it will require a minimum of nailing to hold them, and of labor 
to make and handle them. Forms are constructed of the cheaper 
grades of lumber. To secure a smooth surface, the planks are planed 
on the side on which the concrete will be placed. Green lumber is 
preferable to dry, as it is less affected by wet concrete. If the surface 
of the planks that is placed next to the concrete is well oiled, the 
planks can be taken down much easier, and, if they are kept from the 
sun, can be used several times. 

Crude oil is an excellent and cheap material for greasing forms, 
and can be applied with a white- 
wash brush. The oil should be 
applied every time the forms are 
used. The object is to fill the pores 
of the wood, rather than to cover 
it with a film of grease. Thin soft- 
soap, or a paste made from soap 
and water, is also sometimes used. 

In constructing a factory 

building of two or three stories, Fig . 152 . -century" Cement Brick Machine. 

usually the same set of forms are 

used for the different floors; but when the building is more than four 
stories high, two or more sets of forms are specified, so as always to 
have one set of forms ready to move. 

The forms should be so tight as to prevent the water and thin 
mortar from running through, and thus carrying off the cement. 
This is accomplished by means of tongued-and-grooved or beveled- 
edge boards (Fig. 153) ; but it is often possible to use square lumber 
if it is thoroughly wet so as to swell it before the concrete is placed. 
The beveled-edge boards are often preferred to tongued-and-grooved 
boards, as the edges tend to crush as the boards swell, and beveling 
prevents buckling. 

Lumber for forms may be made of 1-inch, 1^-inch, or 2-inch 
plank. The spacing of studs depends in part upon the thickness of 




298 MASONRY AND REINFORCED CONCRETE 

concrete to be supported, and upon the thickness of the boards on 
which the concrete is placed. The size of the studding depends upon 
the height of the wall and the amount of bracing used. Except in 
very heavy or high walls, 2 by 4-inch or 2 by 6-inch studs are used. 
For ordinary floors with 1-inch plank, the supports should be placed 
about 2 feet apart; with ljUinch plank, about 3 feet apart; and 
with 2-inch plank, 4 feet -apart. 

The length of time required for concrete to set depends upon the 
weather, the consistency of the concrete, and the strain which is to 
come on it. In good drying weather, and for very light work, it is 
often possible to remove the forms in 12 to 24 hours after placing the 
concrete, if there is no load placed on it. The setting of concrete is 
greatly retarded by cold or wet weather. Forms for concrete arches 
and beams must be left in place longer than in wall work, because of 
the tendency to fail by rupture across the arch or be'am. In small, 

^_ ^___ circular arches, like sewers, 

the forms may be removed 
in 18 to 24 hours if the 





Fig. 153. Tongued-and- Beveled Edge. concrete is mixed dry; but 



Grooved Edge. 



if wet concrete is used, in 24 
to 48 hours. Forms for large arch culverts and arch bridges are 
seldom taken down in less than 14 days; and it is often specified that 
they must not be struck for 28 days after placing the last concrete. 
In ordinary floor construction, consisting of slabs, girders, and beams, 
the forms are usually left in place at least a week. 

352. Forms for Columns. In constructing columns, the forms 
are usually erected complete, the full height of the columns; and con- 
crete is dumped in at the top. The concrete must be mixed very 
wet, as it cannot be rammed very thoroughly at the bottom, and care 
must be taken not to displace the steel. Sometimes the forms are 
constructed in short sections, and the concrete is placed and rammed 
as the forms are built. The ends of the bottom of the forms for the 
girders and beams, are usually supported by the column forms. To 
give a beveled edge to the corner of the columns, a triangular strip 
is fastened in the corner of the forms. 

Fig. 154y1 shows the common way, or some modification of it, of 
constructing forms for columns. The plank may be l inch, 1 1 inches, 
or 2 inches thick; and the cleats are usually 1 by 4 inches and 2 by 4 



MASONRY AND REINFORCED CONCRETE 



299 



Si 



inches- The spacing of the cleats depends on the size of the columns 
and the thickness of the vertical plank. 

Fig. 154 J5 shows column forms similar to those used in construct- 
ing the Har- 
vard stadium. 
The planks 
forming each 
side of the 
column are 
fastened to- 
g e t h e r by 
cleats, and 
then the four 
sides are fast- 
ened together 
by slotted 
cleats and 
steel tie-rods. 
These forms 
can be quickly 
and easily re- 
moved. 

Fig. 155 
shows a col- 
umn form in 
which con- 
crete is placed 
and rammed 
as the form is 
constructed. 
Three sides 
are erected to 



b& 



W 




£i 




i 



\ 



\\WWN~=K\WW [ 



5?5E^ 



^=a?4< 



~W 



Fig. 154. Forms for Columns. A— Common method of construction; 
B— Method used in constructing Harvard Stadium. 



the full height, and the steel is then placed. The fourth side is built 
up with horizontal boards as the concrete is placed and rammed. 

Round columns are often desirable for the interior columns of 
buildings. Fig. 156 shows a form that has been used for this type 
of column. The columns for which these forms were used were 20 
inches in diameter, and had a star-shaped core made of structural 



300 



MASONRY AND REINFORCED CONCRETE 



I 



i^ 35==a a ysq 



steel. The forms for each column were made in two parts and bolted 
together. The sides were made of 2 by 3-inch plank surfaced on all 
four sides, beveled on two, and held in place by 
the steel bands, which were J by 2 \ inches and 
spaced about 2\ feet apart. One screw in the 
outer plank at each band of both parts, to- 
gether with a few intermediate screws, held the 
\ 1X4 ° 

^j . p-jJ plank in place. The building for which these 

forms were made was ten stories in height. 
Enough forms were provided for two stories, 
which was sufficient, as they could be removed 
when the concrete had been in place one week. 
Later these same forms were used in construct- 
ing the interior columns of a six-story building. 
Some difficulty was experienced in removing 
these forms, owing to the concrete sticking to 
the plank. But had these forms been made in 
four sections, instead of two, and well oiled, it is 
thought that this trouble would have been 
avoided. Columns constructed with forms as 
shown in Fig. 156 will not have a round sur- 
face, but will consist of many flat surfaces, 
2\ inches wide. If a perfectly round column 

is desired, it will be necessary to cut the surface of the plank next to 

the concrete to the desired radius. 

Forms for octagonal columns can be 

made in a somewhat similar manner to 

these just described. 

353. Forms for Beams and Slabs. 

A very common style of form for beam 

and slab construction is shown in Fig. 

157. The size of the different mem- 
bers of the forms depends upon the 

size of the beams, the thickness of the 

slabs, and the relative spacing of some 

of the members. If the beam is 10 by 

_ _ . . , , . , . . . , ^ . ,' Fig. 156. Form for Round Column. 

20 inches, and the slab is 4 inches thick, 

then 1-inch plank supported by 2 by 6-inch timbers spaced 2 feet 



^^^\V^A 



Fig. 155. Form for 
Column. 




MASONRY AND REINFORCED CONCRETE 



301 



apart, will support the slab. The sides and bottom of the beams 
are enclosed by lj-inch or 2-inch plank supported by 3 by 4-inch 
posts spaced 4 feet apart. 

In Fig. 158 are shown the forms for a reinforced-concrete slab, 
with I-beam construction. These forms are constructed similarly 
to those just described. 

A slab construction supported on I-beams, the bottom of which 

Z" 



r 



psl 



fegsssg s 



S.WiVHsVA'vM 1 ^ 



-^-^sss\s^.\\\v^r-==rK 



2X6" 



-rk4" 



2x4" 



jsa 



4-3x4 



Fig. 157. Forms for Beams and Slabs. 

is not covered with concrete, may have forms constructed as shown 
in Fig. 159. This method of constructing forms was designed by 
by Mr. William F. Kearns (Taylor and Thompson, "Plain and Rein- 
forced Concrete"). 

The construction of forms for a slab that is supported on the top 




feVlWrfWBS 



2xe 



1X4 



2X4 




3;*4" 

Fig. 158. Forms for Reinforced-Concrete Slab Supported by I-Beams. 

of I-beams is a comparatively simple process, as shown in Fig. 160. 
In any form of I-beam and slab construction, the forms can be con- 
structed to carry the combined weight of the concrete and forms. 
When the bottom of the I-beam is to be covered with concrete, it is 
not so easily done as when the haunch rests on the bottom flange 
(Fig. 159) or is a flat plate (Fig. 160). 

354. Forms for Locust Realty Company Building. The forms 
used in constructing the building for the Locust Realty Company (the 
mixing plant has already been described), present one rather unusual 



302 



MASONRY AND REINFORCED CONCRETE 




wr-^ 



Fig. 159. 



i| Bolts) 

Form for Reinforced-Concrete Slab 
between I-Beams. 



V^tz^ss\sh^^-K^\\ 



k^^k^sLVVVS^>^k^ 



2"Plan"k 



Fig. 160. Form for Floor-Slab on I-Beams. 



feature. The lumber for the slabs, beams, girders, and columns was 
all the same thickness, 1J inches. Fig. 161 shows the details of the 
forms for the beams and slabs. The beams are spaced about 6 feet 

apart, and are 8 by 16 inches; 
the slab is 4 inches thick. A 
notch is cut into the 1 by 
6-inch strip on the side of 
the beams, to support the 2 
by 4-inch strip under the 
plank which supports the 
concrete for the slab. The 
posts supporting the forms 
are 3J by 3J-inch, and are 
braced by two 1 by 6-inch 
boards spaced about 3 feet 
apart, and extending in the 
direction of the beams. 
Fig. 162 shows the forms 
for the columns. The planks for each side of the column are held 
together by the 1 by 4-inch strip, and, when erected in place, are 
clamped by the 2 by 4-inch strip. A large opening is left at the 
bottom of each column, so that 
all shavings and sawdust can be 
removed. This opening is closed 
just before the concrete is de- 
posited. 

355. Cost of Forms for 
Buildings. An analysis of the cost 
of forms for an eight-story build- 
ing is given by R. E. Lamb (Con- 
crete Engineering, December, 
1907). The basis of his estimate 
is made on using f-inch by 6-inch 
tongued-and-grooved lumber for 
slab forms ; 1 f -inch dressed plank 
for the sides and bottom of the 

beams and girders; posts 4 by 4-inch spaced 6 feet center to center; 
and on the fact that it cost $20.00 per thousand feet of lumber to make 



WSSS« 



/XJ^-' 



32X3 2 



Fig. 161. Beam and Slab Forms for Locust 
Realty Company Building. 



<Z X4- 



Sl4-*6 



3z 



MASONRY AND REINFORCED CONCRETE 



3(X 



and set one floor 
of forms; that it 
cost $15.00 per 
thousand feet to 
strip the forms 
and reset them 
on the next floor; 
and that it cost 
about $8.00 per 
thousand feet to 
strip the forms 
and lower them 
to the ground. 

With the 
size of the beams 
and girders as 
shown in Fig. 
163, Mr. Lamb 
states that it will 
take an average 
of 4 feet, board 
measure, to erect 
each square foot 
of floor area. The 
basis of his esti- 
mate is as fol- 
lows: that 1.5 
board feet of 
lumber per 
square foot of 
floor is required 
for the slab; that 
for every square 
foot of beam sur- 
face, including 
the bottom, 3.2 
board feet per 
square foot is re- 



M 



« 



i [i 




Fig. 



Column Forms for Locust Realty 
Company Building. 



. ! 

i i 

i i 

i i 

i i 

i j 

I ITxld" "j 

!» ■ i 

IS! « 

■ • I 

"x/d'' 



o 



/fl-0" 



304 MASONRY AND REINFORCED CONCRETE 

quired; and that for each square foot of girder, including the bottom, 
3.6 board feet of lumber is required. Taking these figures, for the 
panel shown, the slab will require 1.5 board feet per square foot; the 
beams, which are 8 by 18-inch, will have 3 feet 8 inches of surface 

per linear foot; and multiplying 

V LJ ■ U this by 3.2 board feet per square 

foot, and dividing by 7.5 feet, the 
distance center to center of 
beams, we find that 1.56 board 
feet per square foot of floor sur- 
face is required. Taking the 
girder in the same way, with 4 
feet 8 inches of surface, multi- 
plied by 3.6 board feet, and 
divided by 18 feet, the distance 
center to center of girders, we find 
that .94 board foot per square foot of floor is required. The total 
of the lumber required, then, is 1.5 board feet for the slab, 1.56 
board feet for the beam, and .94 board foot for the girders — a total 
of 4 board feet per square foot of floor area. 

In this estimate for an eight-story building, three sets of forms 
were used: 

Roof: Stripping the sixth floor, resetting, altering to form valleys, and 
finally stripping roof and lowering forms to ground, 4 board feet 
at 2.6 cents % .104 

Eighth Floor: Stripping the fifth floor, resetting, and finally stripping 

and lowering forms to ground, 4 board feet at 2.3 cents . 002 

Seventh Floor: Stripping the fourth floor, resetting, and finally 

stripping and lowering forms to ground, 4 board feet at 2.3 cents . 092 

Sixth Floor: Cost, same as for the fourth floor . 0G0 

Fifth Floor : Cost, same as for the fourth floor . 060 

Fourth Floor: Stripping the first floor, and resetting, 4 board feet 

at 1.5 cents .060 

Third Floor: Cost, same as for the first floor .184 

Second Floor: Cost, same as for the first floor . 1S4 

First Floor: Making and setting forms, 4 board feet at 

2 cents $.080 

Materia], 4 board feet at 2.6 cents .104 1 84 

9 ) 1 .020 

Average cost per square foot of surface $ 113 

To this average cost of 11.3 cents, 10 per cent should be added for 

waste, breakage, nails, etc.; and if two sets of forms are used, the 



MASONRY AND REINFORCED CONCRETE 305 

third floor would cost 6 cents per square foot, and the seventh floor 

6 cents, giving an average of 9.6 cents per square foot. 

In estimating the cost of the forms for the columns, it is assumed 

that making and placing the forms for the basement columns will cost 

about $26.00 per thousand; the cost of stripping and resetting, 

$16.00 per thousand; and 3.1 square feet of lumber is required for 

each square foot of column surface. 

Eighth Story: Stripping sixth story, resetting and altering, finally 
stripping eighth story, and lowering to ground 3.1 board feet at 
2.2 cents $.068 

Seventh Story: Stripping fifth story, resetting, and finally stripping 

and lowering to ground 3.1 board feet at 1 9 cents .059 

Sixth Story: Cost, same as second story .050 

Fifth Story: Cost, same as second story .050 

Fourth Story: Cost, same as second story .050 

Third Story: Cost, same as second story .050 

Second Story: Stripping basement columns and resetting 3.1 board N 

feet at 1.6 cents .050 

First Story: Cost, same as for the basement columns . 162 

Basement: Material, 3.1 board feet at 2.6 cents $ .081 

Making and setting 3.1 board feet at 2.6 cents .081 

.162 .162 



9) .701 



Average cost per square foot of surface $ . 077 

To this average cost of 7.7 cents per square foot of column surface, 
should be added 10 per cent for bolts, nails, waste, etc. If three sets 
of forms are required, the second-story cost would be 16.2 cents, and 
the sixth story 5.9 cents, giving the average cost per square foot, of 
9.1 cents. 

The student should remember that this lumber has a value 
after it has been removed from the building, and that this value 
should be deducted from the total cost of the forms, to find the actual 
cost of forms. 

356. Cost of Forms for Garage. Some interesting cost data are 
given by Mr. Reygondeau de Gratresse, Assoc. M. Am. Soc. C. E. 
(Engineering-Contracting, October 30, 1907), on the cost of forms 
used in erecting a reinforced-concrete garage in Philadelphia during 
the summer of 1907. The building was 53 feet wide, 200 feet long, 
and four stories high; also there was a mezzanine floor. Tongued- 
and-grooved lumber J inch thick was used for the slab forms, and 
If -inch plank for the beams and girders. 



306 MASONRY AND REINFORCED CONCRETE 

The area of the 1,740 cubic yards of concrete covered by forms 
was* SqFt - 

Footings 4,000 

Columns 20,000 

Floors and Girders 70,000 

Total 94,000 

For this work, 170,000 feet, board measure, of new lumber was 
bought; and 50,000 feet board measure of old lumber was used, 
the cost being: 

50,000 ft. B. M. at $13 $ 650 

170,000 ft. B. M. at $26 4,420 

220,000 ft. B. M. at $23 $5,070 

Since 220,000 feet, board measure, were used for the 1,740 
cubic yards, there were 126 feet, board measure, per cubic yard of 
concrete. 

New forms were made for each floor, except the sides of the 
girders, which were used over for each floor, where the sizes would 
admit of this being done. The props under the girders were allowed 
to remain in place throughout the building until the entire job was 
completed. The forms for the roof were made entirely of the material 
used on the floors below. The area of concrete covered by the new 
lumber was approximately 80,000 square feet. This gives a cost for 
lumber of 6.4 cents per square foot. 

A force of fifteen carpenters working under one foreman, framed, 
erected, and tore down all forms. Laborers handled all the lumber 
for the carpenters, except when they were at work mixing and placing 
concrete. The foreman was paid $35 per week, while the carpenters 
were paid an average of $4.40 for an 8-hour day. Laborers were 
paid 17 cents per hour, and worked a 10-hour day. Over the laborers 
was a foreman who received the same wages as the boss carpenter. 
The forms for a floor were erected in from 8 to 10 days. For the 
framing, erecting, and tearing down of the forms, the labor cost was 
about $3,480, which gives a cost of $2 per cubic yard. For the 
carrying and handling of the lumber, the cost was about $1,914, 
which gives a cost of $1.10 per cubic yard. This gives a total cost 
per cubic yard of forms as follows: 





Per Cu. Yd 


Lumber, 120 ft. B. M. 


$2.90 


Framing, erecting, and tearing down 


2.00 


Handling lumber 


1.10 


Total 


$6.00 



MASONRY AND REINFORCED CONCRETE 



307 



This cost is high, owing to the fact that so- little of the lumber 
was used a second time, there being only from 16 to 20 per cent so 
used. For the 220,000 feet, board measure, of lumber used on the job, 
the average cost per thousand for the forms was: 





Per M. 


Lumber 


$23.00 


Framing, erecting, and tearing down 


15.67 


Handling lumber 


8.70 


Total 


$47.37 



The cost per square foot of concrete for the area covered by forms 

was: 

Lumber $0,064 

Labor 0.057 

Total $0,121 

The cost per cubic yard for lumber and labor was: 

Lumber $2.90 

Labor on forms 3.10 

$6.00 
It should be remembered that the lumber used in the forms 

■24-36- — ■ H 



# 



i_ 



1 E 



o 



Hi" H 




4/fw- 



Tn 



\nz 



.Q 



'I 
I"- 

TV 



3 



Fig. 164. Adjustable Clamp. 

had a salvage value, for which no allowance is made in the above $2.90. 

357. An Adjustable Clamp. Fig. 164 illustrates an adjustable 
clamp for holding forms together. It is commonly used to hold the 
plank forming the sides of a beam or girder in place; it is used also 
in clamping the opposite sides of columns. It is forged from a 1|- 
inch by f-inch steel bar, and is held in place by the slotted forging, 
1 inch square, by driving it tight. 

358. Forms for Conduits and Sewers. Forms for conduits and 
sewers must be strong enough not to give way, or to become deformed, 



308 MASONRY AND REINFORCED CONCRETE 

while the concrete is being placed and rammed; and must be rigid 
enough not to warp from being alternately wet and dry. They must 
be constructed so that they can readily be put up and taken down, 
and can be used several times on the same job. The forms must 
give a smooth and even finish to the interior of the sewer or conduit. 
This has been accomplished on several jobs by covering the forms 
with light-weight sheet iron. 

These forms are usually built in lengths of 16 feet, with one 
center at each end, and with three to five (depending on the size of 
the sewer or conduit) intermediate centers in the lengths of 15 feet. 

The segmental ribs are bolted 
together. The plank for these 
forms are made of 2 by 4-inch 
material, surfaced on the outer 
side, with the edge beveled to the 
radius of the conduit. The seg- 
mental ribs are bolted together, 
and are held in place by wooden 
ties 2 by 4 inches or 2 by 6 inches. 
359. Forms for Torresdale 
Filters. In constructing the Tor- 
resdale filters for supplying Phila- 
delphia with water, several large 
sewers and conduits were built of concrete and reinforced with ex- 
panded metal. In section the sewers were round and the conduits 
were horseshoe-shaped, with a comparatively flat bottom. The 
sewers were 6 feet and 8 feet 6 inches in diameter, and the forms were 
constructed similarly to the forms shown in Fig. 165, except that at 
the bottom the lower side ribs were connected to the bottom rib by 
a horizontal joint, and the spacing of the ribs was 2 feet 6 inches, 
center to center. Fig. 166 shows the form for the 7-foot 6-inch 
conduit. The centering for the 9-foot and 10-foot conduits was con- 
structed similarly to the 7-foot 6-inch conduit, except that the ribs 
were divided into 7 parts instead of 5 parts as shown in Fig. 166. The 
spacing of the braces depended on the thickness of the lagging. For 
lagging 1 inch by 2 J inches, the braces were spaced 18 inches, center 
to center; and for 2 by 3-inch lagging, the spacing of the bracing 
was 2 feet 6 inches. 




Fig. 165. Center for Round Sewer. 



MASONRY AND REINFORCED CONCRETE 



309 



These forms were constructed in lengths of 8 feet. The lagging 
for the smaller sizes of the conduits was 1 inch by 2 J inches, and for 
the larger sizes 2 inches by 3 inches, all of which was made of dressed 
lumber and covered with No. 27 galvanized sheet iron. The bracing 
of the forms was arranged to permit the centering being taken apart 
and brought forward through the sections set in front of it. Three 
sets of these forms 




Fig 



Space 
Wadges 7d pared j'toa' 



Ribs and Braces 
j paced /Q"c. 



f0olt 



Form for Construction of Horseshoe-Shaped 
Concrete Conduit. 



were required for 
each conduit. The 
specifications re- 
quired that the cen- 
tering be left in 
place for at least 60 
hours after the con- 
crete had been 
placed. It was also 
required that this 
work should be con- 
structed in monoli- 
thic sections — that is, the contractor could build as long a section as 
^^ ^^ he could finish in a 

^ijlj H day; and that the 

,..\ sections should be 
securely keyed to- 
gether. 

360. The Blaw 
Steel Forms. The 
Blaw collapsible 
steelforms,asshown 
in Fig. 167, appear 
to be the only suc- 
cessful steel forms 
.,. c\ _- -- so far in general use. 

Fig. 167. Collapsible Steel Center or Form. There have been 

many attempts to devise steel centering for column, girder, and slab 
construction, but no available system has yet been invented. The 
main trouble of those used is their liability to leak, tendency to 
rust, and liability to injury by dents in removing. 




310 



.MASONRY AND REINFORCED CONCRETE 



The Blaw collapsible steel centering is in general use for sewer 

and conduit construction. This 
centering consists of one or 
more steel plates about J inch 
thick and bent to the shape 
required by the interior of the 
sewer to be constructed. The 
steel plates are held in shape 
by angle irons. When set in 
position, the sections are held 
rigid by means of turnbuckles, 
which also facilitate the col- 
lapsing of the sections. The 
adjacent sections are held to- 
gether by staples and wedges, 
the former being riveted to the 
plates. The sections are usu- 
ally made five feet long, and in 
any desired shape or size re- 
quired for sewer or conduit 
work. When these forms are 
used to construct concrete 
sewers or conduits, the surface 
of the forms must be well 
coated with grease or soap to 
prevent the concrete from ad- 
hering to the steel. 

361. Forms for Walls. 
The forms for concrete walls 
should be built strong enough 
so that they will retain their 
correct position while the con- 
crete is being placed and ram- 
med. In high, thin walls, a 
great deal of care is required 
to keep the forms in place so 
that the wall will be true and 

Fig. 168. Forms for Wall. straight. 




MASONRY AND REINFORCED CONCRETE 311 

Fig. 168 shows a very common method of constructing these 
forms. The plank against which the concrete is placed is seldom 
less than 1J inches thick, and is usually 2 inches thick. One-inch 
plank is sometimes used for very thin walls; but even then, the 
supports must be placed close. The planks are generally surfaced 
on the side against which the concrete is placed. The vertical 
timbers that hold the plank in place will vary in size from 2 inches 
by 4 inches to 4 inches by 6 inches, or even larger, depending on the 
thickness of the wall, spacing of these vertical timbers, etc. The 
vertical timbers are always placed in pairs, and are held in place 
usually by means of bolts, except for thin walls, when heavy wire 
is often used. If the bolts are greased before the concrete is placed, 
there is usually not much trouble experienced in removing them. 
Some contractors place the bolts in short pieces of pipe, the diameter 
of the pipe being about -| inch greater than that of the bolt, and 
the length equal to the thickness of the wall. When the bolts are 
removed, the holes are rilled with mortar. 

CENTERS FOR ARCHES 

362. The centers for stone, plain concrete, and reinforced- 
concrete arches are constructed in a similar manner, A reinforced- 
concrete arch of the same span and designed for the same loading, 
will not be so heavy as a plain concrete or stone arch, and the centers 
need not be constructed so strong as for the other types of arches. 
One essential difference in the centering for stone arches and that for 
concrete or reinforced-concrete arches, is that centering for the latter 
types of arches serves as a mould for shaping the soffit of the arch- 
ring, the face of the arch-ring, and the spandrel walls. 

The successful construction of arches depends nearly as much 
on the centers and their supports as it does on the design of the arch. 
The centers should be as well constructed and the supports as un- 
yielding as it is possible to make them. When it is necessary to use 
piles, they should be as well driven as permanent foundation piles, 
and the load should not generally be heavier than that on permanent 
piles. 

363. Classes of Centers. There are two general classes of 
centers — those which act as a truss; and those in which the support, 
at the intersection of braces, rests on a pile or footing. Trusses are 



312 



MASONRY AND REINFORCED CONCRETE 



used when it is necessary to span a stream or roadway. Sometimes 
the length of the span for the centering is very short, or there are a 
series of short spans, or the span may be equal to that of the arch. 
The trusses must be carefully designed, so that the deflection and 
deformation due to the changes in the loading will be reduced to a 
minimum. By placing a temporary load on the centers at the crown, 
the deformation during construction may be very greatly reduced. 
This load is removed as the weight of the arches comes on the centers. 
For the design of trusses, the reader is referred to instruction papers 
or other treatises on Bridge Engineering and Roof Trusses. 

The lagging for concrete arches usually consists of 2 by 3-inch 
or 2 by 4-inch plank, either set on edge or laid flat, depending on 
the thickness of the arch and spacing of the supports. The surface 
on which the concrete is laid is usually surfaced on the side on which 
the concrete is to be placed. The lagging is very often supported 
on ribs constructed of 2 by 12-inch plank, on the back of which is 

placed a 2-inch plank cut to a 
curve parallel with the intrados. 
These 2 by 12-inch planks are set 
on the timber used to cap the 
piles, and are usually spaced 
about 2 feet apart. All the sup- 
ports should be well braced. The 
centers should be constructed to 
give a camber to the arch about 
equal to the deflection of the 
arch when under full load. It is 
therefore necessary to make an 
allowance for the settlement of 
centering, for the deflection of the arch after the removal of the center- 
ing, and for permanent camber. 

The centers should be constructed so that they can be easily 
taken down. To facilitate the striking of centers, they are usually 
supported on folding wedges or sand-boxes. When the latter method 
is used, the sand should be fine, clean, and perfectly dry, and the 
boxes should be sealed around the plunger with cement mortar. 
Striking forms by means of wedges is the commoner method. In 
Fig. 169, a shows the type of wedges generally used, although some- 




Fig. 169. Wedges Used in Placing and 
Removing Forms. 



MASONRY AND REINFORCED CONCRETE 



313 



TABLE XXI * 

Safe Load in Pounds Uniformly Distributed for Rectangular Beams, 
One Inch Thick, Long=Leaf Yellow Pine 

Allowable fibre stress, 1,200 pounds per square inch; factor of safety, 6; modulus of 

rupture, 7,200 pounds per squarelinch. 

Safe loads for other factors of safety may be obtained as follows: New safe load = 

Safe load from table X =v? * — t— . 

New factor 











Depth ( 


)F Beam 


in Inches 






Span 
















Deflec- 


in 




















tion Co- 


Feet 


4 


5 


6 


7 


8 


10 


12 


14 


16 


efficient 


4 


533 


833 


1,200 


1,633 


2,133 


3,333 


4,800 


6,533 




.20 


5 


427 


667 


960 


1,307 


1,707 


2,667 


3,840 


5,227 




.31 


6 


356 


556 


800 


1,089 


1,422 


2,222 


3,200 


4,356 




.44 


7 


305 


476 


686 


933 


1,219 


1,905 


2,743 


3,733 




.61 


8 


267 


417 


600 


817 


1,067 


1,667 


2,400 


3,267 




.79 


9 


237 


370 


533 


726 


948 


1,481 


2,133 


2,904 


3,793 


1.00 


10 


213 


333 


480 


653 


853 


1,333 


1,920 


2,613 


3,413 


1.24 


12 


178 


278 


400 


544 


711 


1,111 


1,600 


2,178 


2,844 


1.78 


14 


152 


238 


343 


467 


610 


952 


1,371 


1,867 


2,438 


2.42 


16 


133 


208 


300 


408 


533 


833 


1,200 


1,633 


2,133 


3.16 


18 


119 


185 


267 


363 


474 


741 


1,067 


1,452 


1,896 


4.00 


20 


107 


167 


240 


327 


427. 


667 


960 


1,307 


1,707 


4.94 


22 


97 


157 


218 


297 


388 


606 


873 


1,188 


1,552 


5.98 


24 


89 


139 


200 


272 


356 


556 


800 


1,089 


1,422 


7.12 


26 




128 


185 


251 


328 


513 


738 


1,005 


1,313 


8.35 


28 




119 


171 


233 


305 


476 


686 


933 


1,219 


9.68 


30 




111 


160 


218 


284 


444 


640 


871 


1,138 


11.12 



To find the safe load for beams of hemlock from the above table, the above 
values must be divided by 2 ; for beams of short-leaf yellow pine and white oak, the 
values must be divided by 1.2; for white pine, spruce, eastern fir, and chestnut, the 
values must be divided by 1.71. 

times three wedges are used, as shown by b in the same figure. They 
are from one to two feet long, 6 to 8 inches wide, and have a slope of 
from 1 to 6 to 1 to 10. The centering is lowered by driving back the 
wedges; and to do this slowly, it is necessary that the wedges have a 
very slight taper. All wedges should be driven equally when the 
centering is being lowered. The wedges should be made of hard- 
wood, and are placed on top of the vertical supports or on timbers 
which rest on the supports. The wedges are placed at about the 
same elevation as the springing line of the arch. 

Tables XXI and XXII can be used to assist in the design of the 
different members of the centers for arches. 

364. Safe Stresses in Lumber for Wooden Forms. In Table 
XXI are given the safe loads which may be placed on beams of long- 
leaf yellow pine, of various depths, on various spans. 

*From Handbook of the Cambria Steel Company. 



314 



MASONRY AND REINFORCED CONCRETE 



TABLE XXII * 
Strength of Solid Wooden Columns of Different Kinds of Timber 





Douglas, 


Southern, Long- 




Northern or Short- 






Oregon and 


Leaf or Georgia 




Leaf Yellow Pine, 






Washington 


Yellow Pine, Ca- 


White Oak 


Red Pine, Norway 






Yellow Fir 


nadian (Ottawa) 




Pine, Spruce, East- 






or Pine 


White Pine, (On- 
tario) Red Pine 




ern Fir, Hemlock 




F 
I 


6,000 


5,000 


4,500 


4,000 


3,500 


d 
4 


5,876 


4,897 


4,407 


3,918 


3,428 


6 


5,739 


4,782 


4,304 


3,826 


3,347 


8 


5,566 


4,638 


4,174 


3,710 


3,247 


10 


5,368 


4,474 


4,026 


3,579 


3,132 


12 


5,156 


4,297 


3,867 


3,438 


3,008 


14 


4,937 


4,114 


3,703 


3,291 


2,880 


16 


4,716 


3,930 


3,537 


3,144 


2,751 


18 


4,498 


3,748 


3,373 


2,998 


2,624 


20 


4,286 


3,571 


3,214 


2,857 


2,500 


22 


4,082 


3,402 


3,061 


2,721 


2,381 


20 


3,703 


3,086 


2,777 


2,469 


2,160 


30 


3,366 


2,805 


2,524 


2,244 


1,963" 


36 


2,934 


2,445 


2,200 


1,956 


1,711 


40 


2,690 


2,241 


2,017 


1,793 


1,569 


50 


2,203 


1,835 


1,652 


1,468 


1,285 



To find the load that a wooden column will support per square inch of sectional 
area, from the above table, the length of the column in inches is divided by the least diam- 
eter of the column, and the result is the ratio of length to diameter of the column. From 
this ratio is found the ultimate strength per square inch of section of a column of any- 
kind of wood given in the table. A factor of safety of 5 should be used in finding the size 
of column required; that is, the working load should not be greater than one-fifth of the 
values given in the table. 

The values given in Table XXI are the safe loads in pounds 
uniformly distributed, exclusive of the weight of the beam itself, for 
rectangular beams one inch thick. The safe load for a beam of any 
thickness may be found by multiplying the values given in the tables 
by the thickness of the beam in inches. From the last column, the 
deflection may be obtained, corresponding to the given span and 
safe load, by dividing the coefficient by the depth of the beam in 
inches, which will give approximately the deflection in inches. 

365. Example. If a beam is required to support a uniformly dis- 
tributed load of 4,000 pounds on a span of 10 feet, what would be the dimensions 
of the beam of long-leaf yellow pine, and what would be the deflection? 

Solution. Following the line for beams of 10-foot span, it is 
found that a beam 8 inches deep and 5 inches wide (853 X 5 = 4,265) 



*From Handbook of the Cambria Steel Company. 



MASONRY AND REINFORCED CONCRETE 315 

would support the load of 4,000 pounds, and the deflection would be 
1.24 4-8 = .16 inch. A second solution would be to use a beam 12 
inches deep and 2 inches wide (1,920 X 2 = 3,840); but according 
to the table, this beam would not be quite strong enough, as it would 
only support a load of 3,840 pounds. 

366. Safe Loads on Wooden Columns. The values given in 
Table XXII are based on the formula : 

P=FX 700+15c 



700 + 15c + c 2 ' 

in which, 

P = Ultimate strength of timber in pounds per square inch; 
F = Ultimate crushing strength of timber; 

I = Length of column, in inches; 
d = Least diameter, in inches; 
I ■ 

C = d- 

Example. If a column 10 feet long is required to support a load of 
20,000 pounds, what would be the size of the column required if short-leaf 
yellow pine was used? 

Solution. Dividing the length of the beam in inches by the as- 
sumed least diameter, 6 inches, we have 120 h- 6 = 20, which gives 
the ratio of the length to the diameter. By the table it is shown that 
2,857 pounds is the ultimate strength for a column of short-leaf pine, 
when / -r- d = 20. Assuming a factor of safety of 5, and dividing 
2,857 by 5, the working load is found to be 571 per square inch. 
Dividing 20,000 by 571, it is found that a column whose area is 35 
square inches is required to support the load. The square root of 
35 is 5.9. Therefore a column of short-leaf yellow pine 6 inches 
square will support the load. 

367. Form for Arch at 1 75th Street, New York. In construe ting 
the 175th Street Arch in New York City, the forms were built so 
that they could be easily moved. The arch is elliptical and is built 
of hard-burned brick and faced with granite. The span of the arch 
is 66 feet ; the rise is 20 feet ; the thickness of the arch-ring is 40 inches 
and 48 inches at the crown and springing line, respectively; and the 
arch is built on a 9-degree skew. The total length of this arch is 
800 feet. 

This arch is constructed in sections, the centering being sup- 
ported on 11 trusses placed perpendicular to the axis of the arch and 



316 



MASONRY AND REINFORCED CONCRETE 



having the form and dimensions shown in Fig. 170. The trusses 
are placed 5 feet on centers, and are supported at the ends and 
middle by three lines of 12 by 12-inch yellow pine caps. The caps 
are supported by 12 by 12-inch posts spaced five feet center to center, 
and rest on timber sills on concrete foundations. The upper and 
lower chord members of the trusses are of long-leaf yellow pine, but the 
diagonals and verticals are of short-leaf yellow pine. The lagging 
is 2| by 6-inch long-leaf yellow pine plank. The connections of the 
timbers are made by means of -f-inch steel plates and f-inch bolts 
arranged as shown in the illustration. As it was absolutely necessary 
to have the forms alike, so that they could be moved along the arch 
and at all times fit the brickwork, they were built on the ground from 




-Loose Filler 



Fig. 170. Arch Centers at 175th Street, New York City. 

the same pattern, and hois'ted to their place by two guyed derricks 
with 70-foot booms. 

On the 12 by 12-inch cap was a 3 by 8-inch timber, on which the 
double wedges were placed. When it was necessary to move the 
forms, the wedges were removed, the forms rested on the rollers, and 
there was then a clearance of about 2} inches between the brick- 
work and the lagging. The timber on which the rollers ran was 
faced with a steel plate \ inch by 4 inches. The forms were moved 
forward by means of the derricks. The settlement of the forms 
under the first section constructed was \ inch; and the settlement 
of the arch-ring of that section after the removal of forms, was ] inch.* 

* I! 7i nineering Record, October 5, 1907. 



MASONRY AND REINFORCED CONCRETE 



317 



368. Forms for Bridge at Canal Dover, Ohio.* The details of 
the centering used in erecting one of the 106-foot 8-inch spans of a 
reinforced-concrete bridge over the Tuscarawas River at Canal 
Dover, Ohio, are shown in Figs. 171a and 1716. Besides this span, the 
bridge consisted of two other spans of 106 feet 8 inches each, and a 
canal span of 70 feet. The centering for the canal span was built 




Fig. 171 a. Centers for Bridge at Canal Dover, Ohio. 

in six bents, each bent having seven piles. A clear waterway of 18 

feet was required in the canal span by the State Canal Commissioner, 

and this passage was arranged under the center of the arch. The 

piles were driven by means of a scow. The cap for the piles was a 3 

by 12-inch timber. 

Plank 2 inches thick 

were sawed to the 

correct curvature, 

and nailed to the 2 

by 12-inch joists, 

which were spaced 

about 12 inches 

apart. The lagging 

was one inch thick, 

and was nailed to 

thp rnrvpd nlank Fig. 171 6. Centers for Bridge at Canal Dover, Ohio. 

The wedges were made and used as shown. The centering was 
constantly checked; this was found important after a strong wind. 
The centering for the other two of the main arches was constructed 
similarly to that of the arch shown. 

After some difficulty had been experienced in keeping the forms 
in place during the concreting of the first arch, the concrete for the 

*Engineering Record, February 9, 1907. 




31S MASONRY AND REINFORCED CONCRETE 

other arches was placed as shown in Fig. 172, and no difficulty was 
encountered. Sections 1 and 1 were first placed, then 2 and 2, 
finishing with section 6. 

The concreting on the canal span was begun November 1, and 
finished November 12; and the forms were lowered by means of the 
wedges five weeks later. The deflection at the crown was 0.5 inch, 
and after the spandrel walls were built and the fill made, there was 
an additional deflection of 0.4 inch. In building the forms, an 
allowance of g-J- ¥ part of the span was made, to allow for this deflec- 




Fig. 172. Diagram of Order of Placing Concrete in Bridge at Canal Dover, Ohio. 

tion. The deflections at the crown of the other three arches were 
0.6 inch, 1.45 inches, and 1.34 inches. 

BENDING OR TRUSSING BARS 

369. Bending Details. The full bending details of the bars 
should be made before the reinforcing steel is ordered for any rein- 
forced-concrete work that is to be constructed. It has been the 
common practice for contractors to make these details, if they are 
made; and they may or may not submit them to the designing archi- 
tects or engineers for their approval. Very often the plans or 
specifications do not state how long the bars are to be, or even state 
what lap of the bars is required; or they may not be very definite in 
the number of bars to be turned up in the beams and girders. If 
architects and engineers would make these details and submit them 
with their general drawings, the contractors could then make a very 
definite estimate on the amount of steel required for the work, and 
these details should also assist the contractor in estimating the cost 
of the bending of the bars. With the assistance of these details be- 
ing made very definite, it should not only assist the contractor in 
making his bid on the work, but would often result in better work 
being done. 

The angle at which the diagonal bars are turned up, varies from 
about 10 degrees to 45 degrees, and sometimes to a greater angle than 



MASONRY AND REINFORCED CONCRETE 



319 



45 degrees. A great deal depends upon the length and depth of the 
beam or girder. If the beam is very short and deep, the bars are 
usually turned up at an angle of about 45 degrees, or perhaps a little 
greater; but if the beam is long and shallow, the angle at which these 
bars are turned is very small. This angle, in the average practice, 
is about 30 degrees. 

The bending of the bars is usually a simple matter, and generally 
can be easily and quickly done. If bends of 30 degrees or more, 





■ /xe' 'Plank 






1 


- .-i 1 TV~~ 




A 


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ii "\ IT ■ 


—8 t 


H 


: k/ 


i • ->«pi nr ,b ^£?i J . 


G 




.1 








1 1 1 

! i it ii 





Fig. 173. Plan of Bending Table. 

with short radii, are required of large bars — 1 inch to \\ inches 
square — it is usually necessary to heat the bars. This makes the 
bending more expensive, as it requires the use of forges and black- 
smiths to do the work. 

370. Tables for Bending Bars. The usual outfit for bending the 
bars cold consists of a strong table, a vise, and a lever with two short 
prongs. The outline to which the bar is to be bent is laid out on the 
table, and holes are bored at the point where the bends are to be 
made. Steel plugs 5 inches to 6 inches long are then placed in these 
holes. Short pieces of boards are nailed to the table where necessary, 
to hold the bar in place while being bent. The bar is then placed in 
the position A-B, Fig. 173, and bent around the plugs C and D, and 



KJ2F.-* 



N 



1 



Fig. 174. Lever Bender. 

then around the plugs E and F, until the ends EH and FG are 
parallel to AB. When bends with a short radius are required, the 
bars are placed in the vise, near the point where the bend is wanted, 
and the end of the bar is pulled around until the required angle is 
secured. The vise is usually fastened to the table. The lever 
shown in Fig. 174 is also used in making bends of short radii. This is 



320 



MASONRY AND REINFORCED CONCRETE 





& o/i>«. 




2W" 


*- /2" — > 



^/tftf <?/ /£^te 




Lever 

Fig. 175. The Hunt Bender. 



done by placing the bar between the prongs and pulling the end of 
the lever around until the required shape is secured. 

371. The Hunt Bender. The bar-bending device shown in 
Fig. 175 was devised by Mr. R. S. Hunt, C. E., and has been used 

by him to bend \\- 
inch bars. In bend- 
ing bars of this size, 
it is not necessary 
to heat them; and 
the size of bars that 
can be shaped by 
this bender depends 
largely on the proportions of the materials of which the bender is 
constructed. 

In constructing this device, a timber 10 inches by 10 inches and 
about 10 feet long is supported on posts and well braced, the top of 
the timber being about 3 feet high. A 2 by 4-inch plank is spiked 
on one edge of the 10 by 10-inch timber, the smaller timber extending 
to within 12 inches of the end of the larger, as shown in the figure. 
On the edge of the 2 by 4-inch timber, is fastened a J-inch by 2-inch 
steel strap, which is the same length as the timber to which it is 
fastened. Opposite the end of the timber, and 3 inches from the 
timber, is a steel pin \\ inches in diameter. The lever is usually 
about 3 \ feet long, and made as shown in the figure. 

To bend a bar with this device, the bar is placed against the steel 



Mk 


N s of 
Beams 


/V-° of Bars 
in each Beam 


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Fig. 176. Bending Detail of Bars for a Beam or Girder. 

strap with the point of the bar at which the bend is to be made 
opposite the steel pin. The lever is hooked on the pin, while being 
held at right angles to the bar to be bent. The lug on the lever 
rests against the bar; and by moving the lever towards the end of the 



MASONRY AND REINFORCED CONCRETE 



321 



timber, the required bend is given to the bar. For smaller sizes of 
bars, a washer should be placed over the pin so as to reduce the space 
between the pin and the bar to be bent. 

372. Beams and Girders. Fig. 176 shows the bending details 
of the bars for a beam or girder in which six bars are required for the 
reinforcement three of which are turned up, one at a distance of 3 



C 



J 



D 



Fig. 177. Bars with Hooked Ends. 

feet, and two at a distance of 4 J feet from the center of the span. The 
light lines indicate the depth of the beam, including the thickness of 
the slab; the vertical dash-and-dot lines, the center of the supports of 
the beam; and the heavy full lines, the bars. 

When plain bars are used for reinforced concrete, architects and 
engineers very often 
require that the 
ends of all the bars 
in the beams and 
girders shall be 
hooked as shown in Fig. 177. This is done to prevent the bars from 
slipping before their tensile strength is fully developed. 

373. Slab Bars. To secure the advantage of a continuous 
slab, it is very often required that a percentage of the slab bars, 
usually one-half, shall be turned up over each beam. Construction 




Fig. 178. Slab Bars. 



j*-/-J^*-/-^^ — 2-/0" — ^/ L 2-^/c"-f/ L 2^— 2'-/Q 



W-2^/-J^j 




Bent Bars for Slabs. 



companies have different methods of bending and holding these bars 
in place; but the method shown in Fig. 178 will insure good results, 
as the slab bars are well supported by the two longitudinal bars 
which are wired to the tops of the stirrups. Fig. 179 shows the 
bending details of slab bars, the beams being spaced six feet center to 
center. 



322 



MASONRY AND REINFORCED CONCRETE 



374. Stirrups. Fig. 180 shows the bending of the bars for 
stirrups. The ends of the stirrups rest on the forms and support the 
beam bars, which assist in keeping these bars in place. The ends of 
the stirrups seldom show on the bottom of the slab of the finished 



A 



7 



— a 



re 

cA 



A 



(\ 



i : 





a b 

Fig. 180. Bending of Bars for Stirrups. 

floor. Sufficient mortar seems to get under the ends of the stirrups 

to cover them. Type a is much more extensively used than type b. 

The latter type is generally used when a large amount of steel is 

required for stir- 
rups, or if the stir- 
rups are made of 
very small bars. 

375. Column 
Bands. In Fig. 181 
two types of column 
bands are shown. 
Type a shows bands 

for a square or a round column; and type b, bands for a rectangular 

column. The bar which forms the band is bent close around each 

vertical bar in the columns, and therefore assists in holding these 

bars in place. The bands for the 

rectangular column b are made 

up of two separate bands. 

37G. Spacers. Spacers, Fig. 

182, for holding the bars in place 

in beams and girders, have been 

successfully used. These spacers 

are made of heavy sheet iron. They are fastened to the stirrups by 




Fig. 181. Column Bands. 




Fig. 182. Spacer. 



MASONRY AND REINFORCED CONCRETE 



323 



es 



means of the loops in the spacers. The ends of the 
spacers which project out to the forms of the sides 
of the beams, should be made blunt or rounded. 
This will prevent the ends of the spacers being 
driven into the forms when the concrete is being 
tamped. The number of these spacers required will 
depend on the lengths of the beams; usually 2 to 4 
spacers are used in each beam. 

377. Unit=Frames. Among the patented methods 
of fastening the bars together for beams and girders, 
is the Unit Girder Frame System. The loose bars 
are bent and made into a frame as shown in Fig. 
183. All this work is done in a shop; and the frames 
are sent to where the building is being constructed, 
ready to be placed. The stirrups are made of round 
or flat bars, and are hot-shrunk on the longitudinal 
rods. The girder, beam, or column unit is shipped 
to the site of the building being constructed, bearing 
a tag numbered to correspond with a number on the 
plan showing the proper position of the reinforce- 
ment. 

BONDING OLD AND NEW CONCRETE 
The place and manner of making breaks or 
joints in floor construction at the end of a day's 
work, is a subject that has been much discussed by 
engineers and construction companies. But there 
has not been any general agreement yet as to the 
best method and place of constructing these joints. 
Wherever joints are made, great care should be 
exercised to secure a bond between the new and the 
old concrete. 

378. Methods of Making Bonds. First Method. 
Fig. 184 shows a sectional view of one method of 
making a break at the end of the day's work, which 
has been used very extensively and successfully. 
The stirrups and slab bars form the main bond be- 
tween the old and the new work, if the break is left 
more than a few hours. Short bars in the top of 



=© 



^> 



324 



MASONRY AND REINFORCED CONCRETE 



the slab will also assist in making a good bond; also, an additional 
number of stirrups should be used in the beam where the break is 
to be made. Before the new concrete is placed, the old concrete 
should be well scraped, thoroughly soaked with clean water, and 



Bonding 3 a rj ^'-o'lonq 
(Joint / 



a 



fcmtjt 



m 



Joint 



S: 



Fig. 184. Break in Slab. Fig. 185. Break in Beam. 

given a thin coat of neat cement grout. An objection to this method 
of forming a joint is that the shrinkage in the concrete may cause a 
separation of the concrete placed at the two different times, so that 
water will find a passage. The top coat that is generally placed 

later will greatly as- 
sist in overcoming 



Beam 



I L 



I I 

ifcj 

Si 



Beam — 



Joint 



1^1 



^Bond ing Bars j 5 ] 






Wt 



Bar 



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-Joint 



— this objection. 

379. Second Me- 
thod. A n o t h er 
method of forming 
stopping-places is 
by dividing the 
beam vertically — 
%'*f.? t w>\ that is, making two 
L-beams instead of 
one T-beam, Fig. 
185. Theoretically 
this is a very good 
method, but practically it is found difficult to construct the forms 
dividing the beam, as the steel is greatly in the way. 

380. Third Method. The method of stopping the work at 
the center of the span of the beams and parallel to the girders, has 
been used to some extent. Fig. 186 illustrates this method. Theoret- 
ically the slab is not weakened; and as the maximum bending 
moment occurs at this point, the shear is zero, and therefore the 



Fig. 186. Break in Center of Span. 




)f 22U)0lc/d\/ 



326 



MASONRY AND REINFORCED CONCRETE 



beams are not supposed to be weakened, except for the loss of con- 
crete in tension, and this is not usually considered in the calculation. 
The bottoms of the beams are tied together by the steel that is placed 
in the beams to take the tensile stresses; and there should be some 
short bars placed in the top of these beams, as well as in the top of 
the slab, to tie them together. The objection made in the description 
of the first method — in that any shrinkage in the concrete at the 
joint will permit water to pass through — is greater in the second and 
third methods than in the first. 

REPRESENTATIVE EXAMPLES OF REINFORCE D= 
CONCRETE WORK 



381. Buck Building. Fig. 187 shows the typical structural 
floor-plan, above the first floor, of a building constructed for J . C. Buck 
at Fifth and Apple tree Streets, Philadelphia. The architects were 

Ballinger & Perrot, and the build- 
ing was constructed by Cramp & 
Company, Philadelphia. The 
building has a frontage of 90 feet 
on Fifth Street, and a depth of 
61 feet on Apple tree Street, and 
is seven stories high. The build- 
ing was constructed structurally 
of reinforced concrete, except the 
first floor and the columns in the 
lower floors. The floors were all 
designed to carry 200 pounds per 
square foot. The side walls were 
constructed of light-colored brick, 
and trimmed with terra-cotta. 
The first floor was constructed 
especially to suit the requirements 
of the chemical company that is to 
occupy the building for several years. If this company should leave the 
building when their present lease expires, it will very probably be 
necessary to reconstruct the first floor; and therefore it was con- 
structed of structural steel, as it will be much easier to remove a 



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Fig. 188. Interior Column Footing for 
Buck Building, Philadelphia, Pa. 



MASONRY AND REINFORCED CONCRETE 



327 



together in the usual manner. The 
columns were built in sections of a length 
equal to the height of two stories. The 
extra metal required in this practice was 
very small; and the expense of half the 
joints, if a change of section had been 
made at each floor, was saved. 

The general outline and details of 
these steel cores are illustrated in Fig. 
189. In the exterior columns, the steel 
cores were used in the basement and the 
first, second, and third floors, where neces- 
sary; in the interior columns, they were 
used also in the fourth story, and in two 
columns the structural steel extended to 
the sixth floor line. The exterior columns 




floor constructed of structural steel than one constructed of rein- 
forced concrete. 

The footings for each of the interior 
columns were designed as single footings. 
They were 10 feet square, 30 inches thick, 
and were reinforced as shown in Fig. 188. 

The columns in the basement, first, 
and second floors, were of structural 
steel, and fireproofed with concrete. The 
wall columns were either square or rec- 
tangular in shape; and the interior columns 
were round, being twenty inches in diame- 
ter. The stress allowed in the structural 
steel of these columns was 16,000 pounds 
per square inch of the steel section; but 
no allowance was made for the four small 
bars placed in the column. These steel 
cores were provided with angle brackets 
to support the beams, and with spread 
bases to transmit the stress in the steel 
to the foundation. The cores are com- 
posed of angles and plates, and are riveted 




5*5*2-5 



1X.4X$-/4 



\5x5x,2-5 



\4-X4-Xq-/4 



'6 A 6 b 



£>?. 



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3S 



Fig. 189. Steel Column Core for 
Buck Building, Philadelphia, Pa. 



328 MASONRY AND REINFORCED CONCRETE 




I- 2 0-1 



^? 



Fig 



Fig. 190. Detail of Beams and Girders for Buck Building, Philadelphia, Pa. 

above the structural, steel, and 
also the columns in which struc- 
tural steel was not required, were 
Terra Cot (a m general reinforced with 8 bars 
1 inch square, in the lower floors; 
and this amount of steel was 
gradually reduced to 4 bars 1 
inch square, in the seventh story. 
In the interior columns, the 
reinforcement above the steel 
cores consisted of 8 bars f inch 
square, in the floor just above 
the structural steel; and the 
number of these bars was gradu- 
ally reduced to 4 in the seventh 
floor. 

The floor-slab was 5 inches 
thick, and was reinforced with f- 
inch square bars spaced 6 inches 

(•(Miters, and A-inch bars 




= 22* 



191. Wall Beams, Buck Building, 
Philadelphia, Pa. 



on 



MASONRY AND REINFORCED CONCRETE 



329 



spaced 24 inches on centers, the latter being placed at right angles to the 
former. The roof slab was designed to carry a live load of 40 pounds 
per square foot, and was 3 J inches thick. The reinforcement con- 
sisted of T 5 g-inch bars spaced 6 inches, and the same sized bars spaced 
24 inches at right angles. 

The floor-beams were in general 8 inches wide, and the depth 
below the slab was 18 inches. The amount of reinforcement in the 
beams varied, depending on the length of the beams. Most of the 
beams were reinforced with 2 bars 1 inch square, and 1 bar 1^ inches 
square. The lj- 
inch bar was turned 
up or trussed at the 
ends, and the 1-inch 
bars were straight. 
The roof beams 
were 6 by 12-inch 
below the slab, and 
were reinforced 
with 2 bars f inch 
square, except in 
the longest beams, 
in which 2 bars 1 
inch square were 
required. A f-inch 
bar, 5 feet long, was 
placed in the top of 
all floors and roof 
beams, where they 
were framed into a 
girder. The ends of these bars were turned down. The stirrups 
were made of f-inch round bars, and were spaced as shown in the 
detail of the beam. See Fig. 190. 

The floor girders were 12 by 24-inch below the slab. The span 
of the girders varied from about 18 feet to about 20 feet; and they 
were all reinforced with 6 bars 1 inch square, three of the bars being 
turned up at the ends. Two f-inch square bars were placed in the 
top of the girders over the supports. These bars were 5 feet long, 
and they were hooked at the ends. Bars f inch square, 5 feet, long, 




Fig. 192. Stairs for Buck Building, Philadelphia, Pa. 



330 



MASONRY AND REINFORCED CONCRETE 



were placed in the slab near the top, at right angles to the girders. 
The bars were 12 inches center to center, and were placed over the 
center of the girders. 

The wall beams or lintels on the Fifth Street and Apple tree 
Street sides of the building, are shown in section in Fig. 191. They 
are 9 inches by 24 inches, and are reinforced with 2 bars 1 inch square. 
The wall girders in the side of the building opposite Apple tree Street 
are 14 inches by 24 inches, and are reinforced with 6 bars 1 inch 
square. 

The stairs were constructed as shown in Fig. 192. The struc- 
tural concrete slab was 6 inches thick, and was reinforced with f- 
inch bars. Safety treads 5 J inches in width, and 12 inches shorter 
than the width of the stairs, were set in each step. 

The concrete for the beams, girders, slabs, and footings was a 
1 : 2 J: 5 mixture; and for the columns, a 1 : 2: 4 mixture was required. 
The stone used in this concrete was trap rock. The concrete was 



f" "T 



-E2- 



4-da 



-HO- 



2 



Hutchinson Jt. 

Fig. 193. Structural Floor-Plan of Mershon Building, Philadelphia, Pa. 

mixed in a batch mixer, and the consistency of the mixture was what 
is commonly known as a wet mixture. Square twisted bars were 
used as the reinforcing steel. 

The first, second, and third floors were finished with lj-inch 
maple flooring. The stringers, 2 inches by 3 inches, were spaced 16 
inches apart, and the space between the stringers was filled with 
cinder concrete. The other floors were finished with a one-inch 
coat of cement finish. A cinder fill 2 inches thick was laid on the 
concrete floor-slab, on which was laid the cement finish. The cinder 
concrete consisted of 1 part Portland cement, 3 parts sand, and 7 
parts cinders. The cement finish was composed of 1 part Portland 
cement, 1 part sand, and 1 part J-inch crushed granite. 

382. Mershon Building. Fig. 193 shows the plan of the 
foundations and the typical layout of the structural members for 
each floor of a building constructed by Cramp & Company on the 



MASONRY AND REINFORCED CONCRETE 331 








<VJ 






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n 4 "' »' ».:• 


^ 


4< ^ fl 4 . -» f 


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V* « ft'd ft ■'.! 












>: a ? *'"1f'/-.« "j 













Fig. 194. Detail of Column Footing, Mer- 
shon Building, Philadelphia, Pa. 

south side of Walnut Street, between 
Ninth and Tenth Streets, Philadelphia. 
This building was erected during the sum- 
mer of 1907. It has a frontage of 27 
feet on Walnut Street, and a depth of 
165 feet on Hutchinson Street, and is 
eight stories high. It was constructed 
ior manufacturing and storage purposes, 
and the floors were designed to carry a 
uniformly distributed live load of 200 
pounds per square foot. 

At the time that this building was 
constructed, the Building Code of Phila- 
delphia permitted a working stress of 
500 pounds per square inch in compres- 
sion in concrete, and a tensile strength 
of 16,000 pounds per square inch in the 
reinforcing steel. The concrete could be 
made of any desired proportions that 
would insure an ultimate strength of 
2,000 pounds per square inch. A thick- 



o-£- 





332 



MASONRY AND REINFORCED CONCRETE 





ness of 2 inches of concrete 
was required on the outside 
of the reinforcing steel in col- 
umns, girders, and beams, and 
1 inch on the bottom of floor- 
slabs. The Building Code re- 
quired that all girders, beams, 
and slabs should be considered 
as simple beams supported at 
the ends, no allowance being 
made for continuous construc- 
tion over supports. Owing 
to the building being only 27 
feet wide, interior columns 
were not required, and there- 
fore footings were needed only 
along the two sides of the 
building. The footings along 
the Hutchinson Street side of 
the building were designed as 
isolated footings, as shown in 
the general plans, and detailed 
in Fig. 194. But this type of 
construction could not be used 
to support the columns of the 
opposite side of the building, 
owing to the adjacent prop- 
erty; and therefore a continu- 
ous footing was used. This 
footing, which is 3 feet deep, 
6 feet wide, and reinforced 
with 18 twisted bars If inches 
square, is really an inverted 
beam with a span of 14 feet 
9} inches. In designing this 
inverted beam, the load was 
considered the same as the 



MASONRY AND REINFORCED CONCRETE 



333 



load permitted on the soil, which was 3 J tons per square foot. 
See Fig. 195. 

In designing the columns, a working stress of 500 pounds per 
square inch was allowed for the whole section of the column. The 
steel reinforcement consists of round bars, banded every 12 inches 
with a f-inch bar. The area of the longitudinal bars was less than 
one per cent of the area of the section of the column. The columns 
decreased in size from 32 by 36 inches in the basement to 12 by 28 
inches at the eighth floor. 

All the floor-beams were the same size, being 10 inches wide 
and 18 inches in depth below the slab; but the amount of reinforce- 
ment was varied. In the cross-beams between the columns, the 
reinforcement consisted of 5 twisted bars 1 inch square; but 6 bars 1 





Fig. 196 b. Detail of Girders, Mershon Building. 

inch square were required for the cross-beams between the longi- 
tudinal beams, as the span was 4 to 5 feet longer for most of the floors. 
The detail of the beams between the columns is shown in Fig. 196a. 
The longitudinal beams between the columns were reinforced with 
4 twisted bars 1 inch square, the details of which are given in Fig. 
1965. The stirrups for all the beams were made of f-inch round, 
steel bars. The beams were connected by a 5-inch slab reinforced 
with f-inch square bars spaced 5 inches. 

383. Erben=Harding Company Building. The exterior and 
interior of a factory building, designed and constructed by Wm. 
Steele & Sons Company for the Erben-Harding Company, Phila- 
delphia, are shown in Figs. 197 and 198. This building is 100 feet by 
153 feet, and was constructed structurally of reinforced concrete, 
except that structural steel was used in the columns. The floors and 
columns were designed to support safely a live load of 120 pounds 
per square foot. 



336 



MASONRY AND REINFORCED CONCRETE 



The floor-panels were about 12 feet by 25 feet, the girders having 

a span of about 12 feet, and the beams a span of 25 feet. One 

intermediate beam was placed in each panel, as shown in the interior 

view. The girders were 12 inches wide and 20 inches deep below 

j r am / j the slab, and were reinforced with 

Expanded AfCtalj 4 bars 1 T V inches in diameter. 

The beams were 12 by 18-inch, 
and were reinforced with 4 bars 
1 \ inches in diame ter. The floor- 
slab was 4 inches thick, and was 
reinforced with 3-inch mesh, No. 
10 gauge, expanded metal. 

The columns were all 18 by 
18-inch; but the structural steel 
(4 angles arranged as shown in 
Fig. 199) in the columns was de- 
signed to support the entire load 
on the columns. Four f-ineh 
bars were placed in the columns 
and wrapped with expanded metal. The exterior columns were 
exposed to view on both the exterior and the interior of the building. 
The entire width between the wall columns was filled by triple win- 
dows. The wall beams were constructed flush with the exterior 
surface of the wall 
columns, as shown 
in Fig. 197. The 
space between the 
bottom of the win- 
dows and the wall 
beams was filled 
with white brick. 
The two fire towers 
located at the cor- 
ners of the building 




Fig. 199. Column for Erben-Harding 
Building, Philadelphia, Pa. 



//2 -0 



Mii.ii 



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I | I 

I | I ' ' « 

1 t ; i 1 7V1 

i ' i ! i I i 



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! i i 
i « ■ 



1 JL • 

-r-9-r 



i 



i i 
j .i 






i ' 

r-M 

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. I I ' 

1 I I I I 

I « I I I 

i_ I J- I J- 



ft 



Fig. 200. 



Plan of Shop Building. Swai'thmore College, 
Swarthmore, Pa. 



were also constructed of white brick. 

The floor finish of this building is somewhat unusual. Sills 2 by 
4 inches were laid on the structural floor-slab of concrete, and the 
space between these sills was filled with cinder concrete. On these 



MASONRY AND REINFORCED CONCRETE 



337 



sills was laid a covering of 2-inch tongued-and-grooved plank; and 
on these planks was laid a floor of J-inch maple, the latter being laid 
perpendicular to the 2-inch plank. 




Section 
Fig. 201. Detail of Girder for Shop Building of Swarthmore (Pa.) College. 

384. Swarthmore Shop Building. In constructing the new 
shop building at Swarthmore College, Swarthmore, Pennsylvania, 
in 1906, concrete blocks were used for the side walls, and the floors 
were constructed of reinforced concrete. This building is 49 feet 8 




5 action a- a 
Plan 

Fig. 202. Stairway in Shop Building, Swarthmore College, Swarthmore, Pa. 

inches by 112 feet, and is 3 stories high. The floors were designed 
to carry a live load of 150 pounds per square foot. A factor of safety 
of 4 was used in all the reinforced-concrete construction. 

The columns are located as shown in Fig. 200. The span of the 
girders is 20 feet, except for the three middle bays, in which the span 



338 



MASONRY AND REINFORCED CONCRETE 




is only 10 feet. The 20-foot girders are 14 inches wide, and the depth 
below the slab is 23 inches. The reinforcement consists of 8 bars 
| inch square. The details of these girders are given in Fig. 201. 
The beams are spaced 5 feet center to center. The span of these 
beams is about 16 feet, the width 8 inches, and the depth 12 inches 
below the slab; and the reinforcement consists of 5 bars f inch "square. 
The slab is 4 inches thick, including the top coat of 1 inch, which was 
composed of 1 part Portland cement and 1 part sand. This finishing 
coat was put on before the other concrete had set, and was figured 
as part of the structural slab. The slab reinforcement consisted of 

J-inch bars spaced 4 inches 
on centers, and J-inch bars 
spaced 24 inches at right 
angles to the bars spaced 4 
inches. The columns ranged 
in size from 10 by 10-inch to 
18 by 18-inch, and were rein- 
forced by placing a bar in each 
corner of the column, which 
bars are tied together by \- 
inch bars spaced 12 inches. 
The amount of this steel was 
about one per cent of the total 
area of the column. 

Fig. 202 shows the plans 
of the stairway. The lintels 
were moulded on the ground, 
and placed when the side 
walls had been built to the 
proper height for the lintels to be placed. The size of the 
lintels was varied on the different floors to conform with the architec- 
tural features of the building. The width of the lintels was made the 
same as the thickness of the walls, and therefore both sides of the 
lintels were exposed to view. The lintels were reinforced with 3 
bars } inch square. 

The concrete was composed of 1 part Portland cement, 3 parts 
sand, and 5 parts stone. The stone was graded in size from \ inch 
o 1 inch. " Johnson" corrugated bars were used as the reinforcing 



Fig. 203. Floor Construction in Shop Building 
of Swarthmore (Pa.) College, Showing Con- 
nection of Girder Beams with Column. 



MASONRY AND REINFORCED CONCRETE 



339 



steel. A panel, 16 by 20 feet, of one of the 
floors, was tested by placing a load of 300 
pounds per square foot over this area. The 
deflection was so slight that it could not be 
conveniently measured. In Fig. 203 is given 
a view of the under side of a floor, showing 
the connection of the girder and beams with the 
column. 

There is a criticism that may be made in 
the details of the girder shown in Fig. 201. 
The bars, which are turned up at the end, should 
have been long enough so that the bars could 
be again bent parallel to the floor line and be ex- 
tended through the column. This would have 
tied the girders together in a more secure 
manner; and these bars, being near the top of 
the slab, would have resisted any negative 
bending moment. 

385. Apartment House. In designing a 
reinforced-concrete apartment house which 
was constructed at Juniper and Spruce 
Streets, Philadelphia, it was desirable to have a 
floor system that was flat on the under side, 
except for the beams connecting the columns, 
so as to avoid the expense of a suspended ceil- 
ing. The greatest span of the flat construction 
necessary to avoid having beams in the ceiling 
of the rooms, was about 18 feet. It was at 
first intended to use a slab of reinforced con- 
crete to connect the beams; but, as the Phila- 
delphia Building Code requires that the depth 
of reinforced concrete must be at least three- 
fifths of an inch per foot of span, to fulfil 
this condition a slab much thicker than neces- 
sary for structural purposes was required. The 
Building Code requires that the floors of apart- 
ment houses shall be designed to carry safelv 
70 pounds per square foot. 



-ez- 



m 



*P^ 



92- 



340 



MASONRY AND REINFORCED CONCRETE 



This apartment house is 40 feet by 127 feet, and eight stories in 
height. There is also a basement under the entire building. In taking 
bids on this building, it was found that a steel frame, not including 
the fireproofing, cost more than a reinforced-concrete structure. It 
was therefore decided to construct the building of reinforced con- 
crete. The walls were of brick, except the eighth story, which was 
concrete. The concrete wall is hollow, having a total thickness of 16 
inches; and it is composed of two slabs, each six inches in thickness, 
with an air space of four inches between the slabs. These slabs are 
reinforced with steel bars placed longitudinally and vertically. 

The type of floor construction used is shown in Fig. 204. Rein- 
forced-concrete girders were constructed, connecting the columns; 
and the space between them was filled with small reinforced-con- 
crete beams and plaster blocks. The girders were designed, when 
possible, as T-beams; and as a certain amount of concrete was 

required in the slab to take the 
compression, the hollow block 
construction was omitted for a 
sufficient width on each side of 
the girder to allow for this com- 
pression. This feature is shown 
in Fig. 204. The beams were 4 
inches wide, 6 inches to 8 inches 
deep, depending on the span, and 
were connected with a 2-inch slab 
of concrete. The beams were 
spaced 16 inches center to center, and each beam was rein- 
forced with a 1-inch round bar. The two-inch slab was rein- 
forced with J-inch bars spaced 24 inches; and over the girders and at 
right angles to the girders, f-inch bars 6 feet long were spaced 16 
inches; that is, one of these bars was placed in the top of each of the 
beams. The span of these beams varied from 12 feet to 18 feet. 

A hollow plaster block, 12 inches wide, was used as a filler be- 
tween the concrete beams. These blocks were made of the required 
depth, 6 and 8 inches, and were 12 inches wide at the top and 11 \ 
inches wide at the bottom. The object in sloping the sides of the 
blocks was to key the blocks between the beams. The block, in 
section, is shown in Fig. 205, and is known as the Keystone Fireproof 




Fig 



Section of Plaster Block. 



MASONRY AND REINFORCED CONCRETE 341 

Block. The coefficient of expansion of plaster blocks is very small 
compared with that of the terra-cotta block; and also the plaster 
block is more efficient as a non-conductor of heat. The blocks were 
spaced 4 inches apart, and therefore served as the forms for the sides 
of the beams. The planks on which the blocks were placed were 
spaced 8 inches apart, which made a saving in the amount of lumber 
required for forms. It was found necessary to wet the blocks thor- 
oughly by means of a hose, before the concrete was placed, as the 
dry blocks quickly absorbed the water from the concrete. About one 
per cent of the blocks were broken in handling them. The partitions 
in the building were made with the blocks. When the floor forms 
were removed, the ceilings and walls were plastered. 

On the Juniper Street side, balconies were constructed nearly 
the full length of the house. They are 4 feet wide. Structurally 
they were constructed as cantilever beams, and consist of slabs of 
concrete 6 inches thick and reinforced with J-inch round bars spaced 
6 inches center to center. These balconies are constructed at each 
floor level. In Fig. 204 is shown a cantilever beam with a span of 
6 feet. It is 12 inches wide and 26 inches in depth, and is reinforced 
with 4 bars } inch in diameter. This cantilever supports the ex- 
terior wall and one end of a simple beam of a span of about 16 feet. 

The exterior and interior columns were constructed of concrete, 
and reinforced with plain round bars. The roof construction was 
similar to the floor construction. 

The concrete consisted of a mixture of 1 part Portland cement, 
3 parts sand, and 5 parts stone. The stone was trap rock, broken to 
pass through a f-inch ring, dust screened out; and the sand is known 
as Jersey gravel, which is a bank sand. The reinforcing bars were 
plain round bars of medium steel. 

386. The McNulty Building.* The columns used in the con- 
struction of the McNulty Building, New York City, are a very interest- 
ing feature in this building. The building is 50 feet by 96 feet, and is 
10 stories high, and was one of the first small-column reinforced-con- 
crete buildings erected in New York. The plan of all the floors is 
the same. A single row of interior columns is placed in the center of 
the building, about 22 feet center to center. 

The columns are of the hooped type, and were designed from the 

^Engineering Record, August 15, 1907. 



342 MASONRY AND REINFORCED CONCRETE 

formula approved by the building laws of New York City. The 
formula used was P = 1,600 r + (160,000 Ah -^ P) X r + 6,000 As, 
in which P = the total working load, r = radius of the helix, As = 
the total area of the vertical steel, Ah = sectional area of the hooping 
wire, P = the pitch of the helix. 

The interior columns are cylindrical in form, except those sup- 
porting the roof, which are 12 by 12-inch and are reinforced with 4 
bars | inch in diameter. In all the other stories except the ninth, 
they are 27 inches in diameter. Below the fifth floor the reinforce- 
ment in each of these columns consists of 2-inch round vertical bars, 
ranging in number from seven in the fifth floor to thirty in the base- 
ment, and banded by a 24-inch helix of J-inch wire with a pitch of 1 J 
inches. The vertical bars were omitted between the sixth and tenth 
floors; and the diameter of the helix was gradually decreased, while 
the pitch was increased. In the ninth floor the diameter was reduced 
to 21 inches. 

The wall columns are in general 30 by 26 inches, and support 
loads from 48,000 pounds in the tenth floor to 719,750 pounds in the 
basement. In the sixth story, the reinforcement in these columns 
consists of 3 round vertical bars 2 inches in diameter; and in each of 
the floors below, the number of bars was increased in these columns 
there being 24 in the basement columns. These are spirally wound 
with ^-inch steel Avire forming a helix 23 inches in diameter, with a 
pitch of 2h inches. Above the seventh floor, the columns are rein- 
forced with 4 bars f inch in dameter, and tied together by T 5 g-inch 
wire spaced 18 inches apart. The columns rest on cast-iron shoes, 
which are bedded on solid rock about 2 h feet below the base- 
ment floor. 

The main-floor girders extend transversely across the building, 
and have a clear span of 21 feet. The floor-beams are spaced about 
6 feet apart, and have a span of about 20 feet 6 inches. The sides of 
the beams slope, the width at the bottom being two inches less than 
the width at the under surface of the slab. The reinforcement con- 
sists of plain round bars. The bars for the girders and beams were 
bent and made into a truss (the Unit System) at the shops of the con- 
tractor, and were shipped to the work ready to be put in place. The 
stirrups were hot-shrunk on the longitudinal bars. The helices for 
the columns were wound and attached to some of the vertical rods at 



MASONRY AND REINFORCED CONCRETE 



343 



the shop, to preserve the pitch. The vertical rods in each column 
project 6 inches above the floor line, and are connected to the bar 
placed on it, by a piece of pipe 12 inches long. 

The concrete was a 1:2:4 mixture. Giant Portland cement 
was used, and f-inch trap rock. The placing of concrete was begun 
about the middle of August, 1906, and the building was completed 
December 20. 

387. The McGraw Building. The McGraw Building, New 
York City, completed in 1907, is a good example of a reinforced- 

Jfirruf) for d"Slab and Treads in Section C;C. 
(Jtirrup for Treads ^ 



Elevator 




Ug_ 



--4-/0-* 



VLS 



Section 3-3 



Fig. 206. Stairs for Fridenberg Building. 

concrete building. The building has a frontage of 126 feet and a 
depth of 90 feet, and is 11 stories in height. The height of the roof 
is about 150 feet above the street level. The building was designed 
to resist the vibration of heavy printing machinery. The first and 
second floors were designed for a live load of 250 pounds per square 
foot; for the third floor, 150 pounds per square foot; for the fourth 
floor and all floors above the fourth floor, 125 pounds per square foot, 



344 



MASONRY AND REINFORCED CONCRETE 



All beams and girders were designed as continuous beams, even 
where supported on the outside beams. There was twice as much 
steel over the supports as in the center of the spans. The Building 
Code of the City of New York requires that the moment for con- 

- Wl Wl 

tinuous beams be taken as — at the center of the span, and as — 

" 10 o 

over the support. These values are more than twice the theoretical 

value as computed for continuous beams. 

One very interesting feature of this 
building is that it Was constructed . dur- 
ing the winter. The first concrete was 
laid during September, and the concrete 
work was completed in April. During 
freezing weather, the windows of the 
floors below the floor that was being con- 
structed were closed with canvas; and 
salamanders (open stoves) were distrib- 
uted over the completed floor, and kept in 
constant operation. Coke was used as 
the fuel for the salamanders. The con- 
crete was mixed with hot water, and the 
sand and the stone were also heated. 
After two or three stories had been 
erected, and the construction force was 
fully organized, a floor was completed in 
about 12 days. Three complete sets of 
forms were provided and used. They 
were usually left in place nearly three 
weeks. 

388. Fridenberg Building. In Fig. 
206 are shown the plans of stairs con- 
structed in the Fridenberg building at 908 

Chestnut Street, Philadelphia. This building is 24 feet by 60 feet, 

and is seven stories high. Structurally the building was constructed 

of reinforced concrete. The stair and elevator tower is located in the 

rear of the main building. 

The plans of the stairs are interesting on account of the long-span 

(about 16 feet) slab construction. The stairs were designed to carry 




Fig. 207. Detail of Lintel. 



MASONRY AND REINFORCED CONCRETE 345 

safely a live load of 100 pounds per square foot; and in the theoretical 
calculations the slab was treated as a flat slab with a clear span of 16 
feet. The shear bars were made and spaced as shown in the details. 
The calculations showed a low shearing value in the concrete, but 
stirrups were used to secure a good bond between the steel and con- 
crete. 

The concrete was a 1:2:4 mixture, and was mixed wet. The 
reinforcing steel consisted of square deformed bars, except the stir- 
rups, which were made of J-inch plain round steel. 

389. General Electric Company Building. An interesting 
feature of a large reinforced-concrete building constructed for the 
General Electric Company at Fort Wayne, Ind., is the design of the 
lintels. As shown in Fig. 207, the bottom of the lintel is at the same 
elevation as the bottom of the slab. The total space between the 
columns is filled with double windows; and the space between the 
bottom of the windows and the floor is filled with lintels and a thin 
wall of reinforced concrete, as shown in the figure. 

390. Water=Basin and Circular Tanks. Figs. 208 and 209 
illustrate sections of the walls of the pure water basin and the 50- 
foot circular tanks which have been partly described in Part I under 
the heading of Waterproofing. 

The pure water basin was 100 feet by 200 feet, and 13 feet deep, 
giving a capacity of 1,500,000 gallons. The counterforts are spaced 
12 feet 6 inches center to center, and are 12 inches thick, except every 
fourth one, which was made 18 inches thick. The 18-inch counter- 
forts were constructed as two counterforts 9 inches thick, as the 
vertical joints in the walls were made at this point; that is, the con- 
crete between the centers of two of the 18-inch counterforts was 
placed in one day. On the two ends and one side of the basin, the 
counterforts were constructed on the exterior of the basin to support 
about 10 feet of earth. But on one side it would have been necessary 
to remove rock 6 to 8 feet in thickness to make room for the counter- 
forts, had they been constructed on the exterior of the basin. There- 
fore they were constructed inside of the basin. If both faces of the 
vertical wall had been reinforced, the same as the one shown, then 
the wall would have been able to resist an outward or inward pressure, 
and the "piers" would act as counterforts or buttresses, depending on 
whether they were in tension or in compression. 



346 



MASONRY AND REINFORCED CONCRETE 



The concrete used consisted of 1 part Portland cement, 3 parts 
sand, and 5 parts crushed stone. The stone was graded in size from 
J-inch as the minimum to f-inch as the maximum size. Square- 
sectioned deformed bars were used as the steel reinforcement. The 
forms were constructed in units so that they could be put up and taken 
down quickly. 

The size and spacing of the bars in the walls of the circular tanks, 
are shown in Fig. 209. The framework of the forms to which the 
lagging was fastened was cut to the desired curve at a planing mill. 

k8H 




m .. 



2 Bars £ 
JZQ.C "^ 



^m 






^z 



<3 

-IN 



S3 

a 
"It 



T m?-~~~^ r 



( j Bar j /z'c.c. 
Fig. 208. Section of Water Basin Wall. Fig. 209. Section of Tank. 

This framing was cut from 2 by 12-inch lumber. The lagging was 
\ inch thick, and surfaced on one side. 

391. Main Intercepting Sewer. In the development of sewage 
purification work at Waterbury, Conn., the construction of a main 
intercepting sewer was a necessity. This sewer is three miles long. 
It is of horseshoe shape, 4 feet 6 inches by 4 feet 5 inches, and is con- 
structed of reinforced concrete. The details are illustrated in Fig. 
210. 



MASONRY AND REINFORCED CONCRETE 



347 



Strap Iron 



The trench excavations were principally through water-bearing 
gravel, the gravel ranging from coarse to fine. Some rock was en- 
countered in the trench excavations. It was a granite-gneiss of 
irregular fracture, and cost, with labor at 17 \ cents per hour, about 
$2.00 per cubic yard to remove it. Much trench work has varied 
in depth from 20 to 26 feet. Owing to the varying conditions, it was 
necessary to vary the sewer section somewhat. Frequently the footing 
course was extended. However, the section shown in the figure is 
the normal section. 

The concrete was mixed very wet, and poured into practically 
water-tight forms. The proportions used were \ part Atlas Portland 
cement to 7| parts 
of aggregate, grad- 
ed to secure a dense 
concrete. Care w T as 
used in placing the 
concrete, and very 
smooth surfaces 
were secured. 
Plastering of the 
surfaces was 
avoided. Any voids 
were grouted or 
pointed, and 

smoothed with a Fig. 210. Intercepting Sewer at Waterbury, Conn. 

wooden float. Expanded metal and square twisted bars were used in 
different parts of the work. In Fig. 210, the size and spacing of the 
bars are shown. The bars were bent to their required shape before 
they were lowered into the excavation. 

The forms in general were constructed as shown in the figure. 
The inverted section was built as the first operation; and after the 
surface was thoroughly troweled, the section was allowed to set 36 
to 48 hours before the concreting of the arch section was begun. The 
lagging was f inch thick, with tongued-and-grooved radial joints, and 
toe-nailed to the 2-inch plank ribs. The exterior curve was planed 
and scraped to a true surface. The vertical sides of the inner forms 
are readily removable, and the semicircular arch above is hinged at 
the soffit and is collapsible. The first cost of these forms has averaged 




348 



MASONRY AND REINFORCED CONCRETE 



$18.00 for 10 feet of length; and the cost of the forms per foot of 

sewer built, including first cost and maintenance, averaged 10 cents. 

Petrolene, a crude petroleum, was found very effective in preventing 

the concrete from adhering to the forms. 

A mile and a-half of the sewer has been completed (May, 1908), 

and is in use, all of which has been constructed in water-bearing soil; 

and the greater 
part of it has been 
4 to 12 feet below 
the ground-water 
level. The interior 
surface in this 
length subjected to 
percolation is 118,- 
000 square feet. 
The total seepage 
from this area has 
been less than 0.03 
cubic foot per sec- 
ond. 




' i / "3arj 

/O'C.C. 



■ /2-o — /»(... — 

% Stirrups 

Section of Bronx Sewer, New York. 



Fig. 211. 

Cost records kept under the several contracts and assembled into 

a composite form, show what is considered to be the normal cost of 

this section under the local conditions. Common labor averaged \1\ 

cents, sub-foremen 30 cents, and general foremen 50 cents per hour. 

Normal Cost per Linear Foot of 53 by 54=Inch Reinforced=Concrete 

Sewer 

Steel reinforcement, Yl\ lbs 

Making and placing reinforcement cages 

Wooden interior forms, cost, maintenance, and depreciation 
Wooden exterior forms, cost, maintenance, and depreciation 

Operation of forms 

Coating oil 

Mixing concrete 

Placing concrete 

Screeding and finishing invert 

Storage, handling, and cartage of cement 

0.482 bbl. cement at $1.53 

0.17 cu. yd. sand at $0.50 

0.435 cu. yd. broken stone at $1.10 

Finishing interior surface 

Sprinkling and wetting completed work 

Total cost per linear foot $2 . 97 

This is equivalent to a cost of $9.02 per cubic yard. 



.43 
.14 
.12 
.05 
.16 
.01 
.30 
.27 
.08 
.08 
.74 
.09 
.47 
.01 
.02 



MASONRY AND REINFORCED CONCRETE 



349 



392. Bronx Sewer, New York. In Fig. 211 is shown a section 
of one of the branch sewers that is being constructed in the Borough 
of the Bronx, New York City. A large part of this sewer is located 
in a salt marsh where water and unstable soil make construction work 
very difficult. The general elevation of the marsh is 1.5 feet above 
mean high water. In constructing this sewer in the marsh, it is 
necessary to construct a pile foundation to support the sewer The 
foundation is capped with reinforced concrete; and then the sewer, 
as shown in the section, is constructed on the pile foundation. The 
concrete for this work is composed of 1 part Portland cement, 2\ 
parts sand, and 5 parts trap rock. The rock was crushed to pass a 
f-inch screen. "Ransome" twisted bars were used for the reinforce- 
ment in 'this work. 

393. Girder Bridge. The reinforced-concrete bridge shown 
in Fig. 212 was constructed near Allentown, Pennsvlvania, in 1907. 










G3 



Fig. 212, Girder Bridge near Allentown, Pa. 



This type of bridge has been found to be economical for short spans. 
Worn-out wooden and steel highway bridges are in general being 
replaced with reinforced-concrete bridges, and usually at a cost less 
than that of a steel bridge of the same strength. Steel bridges should 
be painted every year; and plank floors, as commonly used in high- 
way bridges, require almost constant attention, and must be entirely 
renewed several times during the life of a bridge. A reinforced-con- 
crete bridge, however, is entirely free of these expenses, and its life 
should at least be equal to that of a stone arch. From an architec- 



350 MASONRY AND REINFORCED CONCRETE 

tural standpoint, a well-finished concrete bridge compares very 
favorably with a cut-stone arch. 

The bridge shown in Fig. 212 is 16 feet wide, and has a clear 
span of 30 feet. It was designed to carry a uniformly distributed 
load of 150 pounds per square foot, or a steel road-roller weighing 15 
tons, the road-roller having the following dimensions: The width 
of the front roller is 4 feet; and of each rear roller, 20 inches; the dis- 
tance apart of the two rear rollers is 5 feet, center to center; and 
the distance between front and rear rollers is 11 feet, center to cen- 
ter; the weight on the front roller is 6 tons, and 4.5 tons on each of 
the rear rollers. 

In designing this bridge, the slab was designed to carry a live 
load of 4.5 tons on a width of 20 inches, when placed at the middle of 
the span, together with the dead load consisting of the weight of the 
macadam and the slab. The load considered in designing the cross- 
beams, consisted of the dead load — weight of the macadam, slab, and 
beam — and a live load of 6 tons placed at the center of the span of the 
beam, which was designed as a T-beam. In designing each of the 
longitudinal girders, the live load was taken as a uniformly distributed 
load of 150 pounds per square foot over one-half of the floor area of 
the bridge. The live load was increased 20 per cent over the live 
load given above, to allow for impact. 

In a bridge of this type, longitudinal girders act as a parapet, as 
well as the main members of the bridge. The concrete for this work 
was composed of 1 part Portland cement, 2 parts sand, and 4 parts 
1-inch stone. Corrugated bars were used as the reinforcing steel. 

When there is sufficient headroom, all the beams can be con- 
structed in the longitudinal direction of the bridge, and are under the 
slab. The parapet may be constructed of concrete; or a cheaper 
method is to construct a handrailing with lj-inch or 2-inch pipe. 




Depositing Concrete for Lining of Aqueduct No. 7. 




Lining of Aqueduct, Completed. 




View of Completed Aqueduct. 
CONSTRUCTION OF AN AQUEDUCT ON LINE OF ILLINOIS AND MISSISSIPPI CANAL 




CONNECTICUT AVENUE BRIDGE OVER ROCK CREEK, WASHINGTON, D. C. 

Largest concrete bridge in world without steel reinforcement. The five principal arches 
have spans of 1.50 feet; highest point of bridge above gorge, 150 feet; each abutment pier com- 
prises two smaller arches. Total length between abutments, 1,341 feet. 



MASONRY AND REINFORCED 
CONCRETE 

PART V 



THEORY OF ARCHES 

394. The mechanics of the arch are almost invariably solved 
by a graphical method, or by a combination of the graphical method 
with numerical calculations. This is done, not only because it simpli- 
fies the work, but also because, although the accuracy of the graphical 
method is somewhat limited, yet, with careful work, it may easily be 
made even more accurate than is necessary, considering the uncer- 
tainty as to the true ultimate strength of the masonry used. The 
development of this graphical method must necessarily follow the 
same lines as in Statics. It is here assumed that the student has a 
knowledge of Statics, and that 
he already understands the graph- 
ical method of representing the 
magnitude, direction, and line of 
application of a force. Several of 
the theorems or general laws re- 
garding the composition and reso- 
lution of forces will be briefly 
reviewed as a preliminary to the 

proof of those laws of graphical Fi S- 213. Resultant of Two Forces. 

statics which are especially applied in computing the stresses in 
an arch. 

395. Resultant of Two Forces. The resultant of two forces, 
A and B, which are not parallel, whose lines of action are as shown 
in Fig. 213a, and which are measured by the lengths of the lines 
A and B in diagram b, is readily found by producing the lines of 
action to their intersection at c. The two known forces are drawn in 

Copyright, 1908, by American School of Correspondence 





352 



MASONRY AND REINFORCED CONCRETE 



diagram b so that their direction is parallel to the known directions 
of the forces, and so that the point of one force is at the butt end of the 
other. Then the line R joining the points m and n in diagram b 
gives the direction of the resultant; and a line through c parallel to 
that direction, gives the actual line of that resultant. The line mn 
also measures the amount of the resultant. Note that diagram b is a 
closed -figure. If an arrow is marked on R so that it points upward, 
the arrows on the forces would run continuously around the figure. 
If R were acting upward, it would represent the force which would 
just hold A and B in equilibrium; pointing downward, it is the re- 
sultant or combined effect of the two forces. We may thus define the 
resultant of two (or more) forces as the force which is the equal and 
opposite of that force which will just hold that combination of forces 
in equilibrium. 

396. Resultant of Three or More Forces. This may be solved by 

an extension of the 
method previously 
given as shown in 
Fig. 213. The re- 
sultant of B and C 
(see Fig. 214) is R'; 
and this is readily 
combined with A, 
giving R tf as the re- 
sultant of all three 
forces. The same 

principle may be extended to any number of non-parallel forces acting 
in a plane. The resultant of four non-parallel forces is best deter- 
mined by finding, first, the resultant of each pair of the forces taken 
two and two. Then the resultant of the two resultants is found, 
just as if each resultant were a single force. 

397. Resultant of Two or More Parallel Forces. When the 
forces are all parallel, the direction of the resultant is parallel to the 
component forces; the amount is equal to the sum of the component 
forces; but the line of action of the resultant is not determinable as 
in the above cases, since the forces do not intersect. It is a principle 
of Statics which is easily appreciated, that it does not alter the statics 
of any combination of forces to assume that two equal and opposite 




Fig. 214. Resultant of Three Forces. 



MASONRY AND REINFORCED CONCRETE 



353 



forces are applied along any line of action. From Fig. 215 b, we see 
that the forces F and G will hold A in equilibrium; that G and H 
will hold B in equilibrium ; and that H and K will hold C in equilib- 
rium. But the force G required to hold A in equilibrium is the 
equal and opposite of the force G required to hold B in equilibrium ; 
and similarly the force H for B is the equal and opposite of the H 
for C. We thus find that the forces A, B, and C can be held in equilib- 
rium by an unbalanced force F, two equal and opposite forces G, 
two equal and opposite forces H, and the unbalanced force K. The 
net result, therefore, is that A, B, and C are held in equilibrium by 
the two forces F and K. The resultant R is the sum of A, B, and C; 
and therefore the combined-load line represents the resultant R.. 
The external lines of diagram b show that F, K, and R form a closed 




Fig. 215. Equilibrium Polygon with Oblique Closing Line. 

figure with the arrows running continuously around the figure; and 
that F and K are two forces which hold R, the resultant of A, B, and 
C, in equilibrium. By producing the lines representing the forces 
F and K in diagram a until they intersect at x, we may draw a vertical 
line through it which gives the desired line of action of R. This is in 
accordance with the principles given in the previous article. 

Nothing was said as to how F, G, H, and K were drawn in a 
and b. These forces simply represent one of an infinite number of 
combinations of forces which would produce the same result. The 
point o is chosen at random, and lines (called rays) are drawn to the 
extremities of all the forces. The lines of force (A, B, and C) in 
diagram b (which is called the force diagram), are together called the 



354 MASONRY AND REINFORCED CONCRETE 

load line. The line of forces (F, G, H, and K) in diagram a, together 
with the closing line yz, is called an equilibrium polygon. 

398. Statics of a Linear Arch. We shall assume that the lines 
in Fig. 215 by which we have represented forces F, G, H, and K 
represent struts which are hinged at their intersections with the forces 
A, B, and C, which represent loads; and that the two end struts F and 
K are hinged at two abutments located at y and z. Then all of the 
struts will be in compression, and the rays of the force dia- 
gram will represent, at the same scale as that employed to repre- 
sent forces or loads A, B, and C, the compression in each of the struts. 
In the force diagram, draw a line from o, parallel with the line yz. It 
intersects the load line in the point n. Considering the triangle opn 
as a force diagram, op represents the force F, while pn and on may 
represent the direction and amount of two forces which will hold F 
in equilibrium. Therefore pn would represent the amount and 
direction of the vertical component of the abutment reaction at y, and 
on would represent the component in the direction of yz. Similarly 
we may consider the triangle onq as a force diagram; that nq repre- 
sents the vertical component R" ', and that on represents the component 
in the direction zy. Since on is common to both of these force tri- 
angles, they neutralize each other, and the net resultant of the two 
forces F and K is the two vertical forces R and E"; but since the 
resultant R is the resultant of F and K, we may say that R r and R" 
are two vertical forces whose combined effect is the equal and 
opposite of the force R. Although an indefinite number of com- 
binations of forces could begin and end at the points y and z, and 
could produce equilibrium with the forces A, B, and C, the forces 
R' and R" are independent of that particular combination of struts, 
F, G, H, and K. 

399. Graphical Demonstration of Laws of Statics by Student. 
The student should test all this work in Statics by drawing figures 
very carefully and on a large scale, in accordance with the general 
instructions as described in the sections, and should purposely make 
some variation in the relative positions and amounts of the forces 
from those indicated by the figures. By this means the student will 
be able to obtain a virtual demonstration of the accuracy of the laws 
of Statics as formulated. The student should also remember that 
the laws are theoretically perfect; and when it is stated, for example, 



MASONRY AND REINFORCED CONCRETE 



355 



that certain lines should be parallel, or that a certain line drawn in 
a certain way should intersect some certain point, the mathematical 
laws involved are perfect; and if the drawing does not result in the 
expected way, it either proves that a blunder has been made, or it 
may mean that the general method is correct,, but that the drawing is 
more or less inaccurate. 

400. Equilibrium Polygon with Horizontal Closing Lines. In 
Fig. 216, have been drawn the same forces A, B, and C, having the 
same relative positions as in Fig. 215. The lines of action of the two 
vertical forces R' and R" have also been drawn in the same relative 
position as in Fig. 215. The point n has also been located on the 

? 




Fig. 216. Equilibrium Polygon with Horizontal Closing Line. 

load line in the same position as in Fig. 215. Thus far the lines are 
a repetition of those already drawn in Fig. 215, the remainder of the 
figure being omitted for simplicity. Since the point n in Fig. 215 is 
the end of the line from the trial pole o, which is parallel to the closing 
line yz, and since the point n is a definitely fixed point and determines 
the abutment reactions regardless of the position of the trial pole o, 
we may draw from n an indefinite horizontal line, such as no' ', and 
we know that the pole of any force diagram must be on this line if 
the closing line of the corresponding equilibrium polygon is to be a 
horizontal line. For example, we shall select a point o' on this line 
at random. From o' we shall draw rays to the points p, s, r, and q. 
From the point y, we shall draw a line parallel to o'p. Where this 
line intersects the force A, draw a line parallel to the ray o's. Where 
this intersects the force B, draw a line parallel to the ray o'r. Where 
this intersects the force C, draw a line parallel to the ray o'q. This 



356 MASONRY AND REINFORCED CONCRETE 

line must intersect the point z , which is on a horizontal line from y. 
The student should make some such drawing as here described, and 
should demonstrate for himself the accuracy of this law. This 
equilibrium polygon is merely one of an infinite number which, if 
acting as struts, would hold these forces in equilibrium, but it com- 
bines the special condition that it shall pass through the points y and 
z'. There are also an infinite number of equilibrium polygons which 
will hold these forces in equilibrium and which will pass through the 
points y and z f . 

We may also impose another condition, which is that the first 
line of the equilibrium polygon shall have some definite direction, such 
as yl. In this case the ray from the point p of the force diagram must 
be parallel to yl; and where this line intersects the horizontal line no' 
(produced in this case), is the required position for the pole o". Draw 
rays from o" to s, r, and q, continuing the equilibrium polygon by lines 
which are respectively parallel to these rays. As a check on the work, 
the last line of the equilibrium polygon which is parallel to o"q should 
intersect the point z' . The triangles ykh and o'pn have their sides 
•respectively parallel to each other, and the triangles are therefore 
similar, and their corresponding sides are proportional, and we may 
therefore write the equation: 

o'n : yh :: pn : kh. 

Also, from the triangles ylh and o"pn, we may write the proportion : 

o"n : yh :: pn : Ih. 

From these two proportions we may derive the proportion : 

o'n : o"n :: Ih : kh; 

but o'n and o"n are the pole distances of their respective force diagrams, 
while kh and Ih are intercepts by a vertical line through the corre- 
sponding equilibrium polygons. The proportion is therefore a proof? 
in at least a special case, of the general law that the perpendicular 
distances from the poles to the load lines of any two force diagrams 
are inversely proportional to any two intercepts in the corresponding 
equilibrium' polygons. The above proportions prove the theorem for 
the intercepts hk and hi. A similar combination of proportions would 
prove it for any vertical intercept between y and //. The proof of this 
general theorem for intercepts which pass through other lines of the 



MASONRY AND REINFORCED CONCRETE 357 

equilibrium polygon, is more complicated and tedious, but is equally 
conclusive. Therefore, if we draw any vertical intercept, such as 
tvw, we may write out the general proportion : 

o"n : o'n : : tw : vw (40) 

In this proportion, if o"n were an unknown quantity, or the position 
of o" were unknown, it could be readily obtained by drawing two 
random lines as shown in diagram c, and laying off on one of them 
the distance no' , and on the other line the distances vw and tw. By 
joining v and o' in diagram c, and drawing a line from t parallel to vo', 
it will intersect the line no' produced, in the point o" . As a check, 
this distance to o" should equal the distance no" in diagram b. A 
practical application of this case, and one that is extensively employed 
in arch work, is the requirement that the equilibrium polygon shall be 
drawn so that it shall pass through three points, of which the abut- 
ments are two, and some other point (such as v) is the third. After 
obtaining a trial equilibrium polygon whose closing line passes through 
the points y and z' , the proper position for the pole o" which shall give 
the equilibrium polygon that will pass through the point v, may be 
easily determined by the method described above. 

The process of obtaining an equilibrium polygon for parallel 
forces which shall pass through two given abutment points and a 
third intermediate point, may be still further simplified by the appli- 
cation of another property, and without drawing two trial equilib- 
rium polygons before we can draw the required equilibrium polygon. 
It may be demonstrated that if the pole distance from the pole to the 
load line is unchanged, all the vertical intercepts of any two equilib- 
rium polygons drawn with these same pole distances are equal. For 
example, in Fig. 215, a line is drawn from o, vertically upward until 
it intersects the horizontal line drawn through n in the point o" . This 
point is the pole of another equilibrium polygon whose closing line 
will be horizontal, because the pole lies on a horizontal line from the 
previously determined point n in the load line. Any vertical inter- 
cept of this equilibrium polygon will be equal to the corresponding 
intercept on the first trial equilibrium polygon; therefore, in order to 
draw a special equilibrium polygon for a given set of vertical loads, 
the polygon to pass through two horizontal abutment points and a 
definite third point between them, we need only draw first a trial equi- 



358 MASONRY AND REINFORCED CONCRETE 

librium polygon, the rays in the force diagram being drawn through 
any point chosen as a pole. Then, if we draw a line from the trial 
pole which shall be parallel with the closing line of this trial equilib- 
rium polygon, the line will intersect the load line in the point n. 
Drawing a horizontal line from the point n in the load line, we have 
the locus of the pole of the desired special equilibrium polygon. Then 
draw a vertical through the point through which the special equilib- 
rium polygon is to pass. The vertical distance of this point above 
the line joining the abutments, is the required intercept of the true 
equilibrium polygon. The intersection of that vertical with the upper 
line and the closing line of the trial equilibrium polygon, is the inter- 
cept of the trial polygon. The pole distance of the true equilibrium 
polygon is then obtained by the application of Equation 46, by which 
the pole distances are declared inversely proportional to any two 
corresponding intercepts of the equilibrium polygons. 

Another useful property, which will be utilized later, and which 
may be readily verified from Figs. 215 and 216, is that, no matter 
what equilibrium polygon may be drawn, the two extreme lines of the 
equilibrium polygon, if produced, intersect in the resultant R; there- 
fore, when it is desired to draw an equilibrium polygon which shall 
pass through any two abutment points, such as yz or yz f , we may draw 
from these two abutment points, two lines which shall intersect at 
any point on the resultant R. We may then draw two lines which 
will be respectively parallel to these lines from the extremities p and 
q of the load lines, their intersection giving the pole of the correspond- 
ing force diagram. 

401. Equilibrium Polygon for Non=Vertical Forces. The 
above method is rendered especially simple, owing to the fact that the 
forces are all vertical. When the forces are not vertical, the method 
becomes more complicated. The principle will first be illustrated 
by the problem of drawing an equilibrium polygon which shall pass 
through the points y, z, and v in Fig. 217. We shall first draw 
the two non-vertical forces in the force diagram. The resultant R 
of the forces A and B is obtained as shown in Fig. 213. Utilizing 
the property referred to in the previous article, we may at once draw 
two lines through y and z which intersect at some assumed point e 
on the resultant R. Drawing lines from p and q parallel respectively 
to ez and ey, we determine the point p f as the trial pole for our force 



MASONRY AND REINFORCED CONCRETE 



359 



diagram. As a check on the drawing, the line joining the inter- 
sections b and c should be parallel to the ray o's, thus again verifying 
one of the laws of Statics. If the line be is produced until it inter- 
sects the line yz produced, and a line is drawn from the intersection x 
through the required point v, it will intersect the forces A and B in 
the points d and g. Then dg will be one of the lines of the required 
equilibrium polygon. By drawing lines from q and p parallel to yd 
and zg, we find their intersection o" , which is the pole of the required 
force diagram. There are two checks on this. result: (1) the line 
so" is parallel to dg; and (2) the line o'o" is horizontal. 

If the line be is horizontal or nearly so, the intersection (x) of 
be and yz produced is at an infinite distance away, or is at least off the 




Fig. 217. Equilibrium Polygon through Three Chosen Points. 

drawing. If be is actually horizontal, the line dg will also be a hori- 
zontal line passing through v. When be is not horizontal, but is so 
nearly so that it will not intersect yz at a convenient point, the line 
dg may be determined as is indicated by the dotted lines in the figure. 
Select any point on the line yz, such as the point o. Through the 
given point v, draw a vertical line which intersects the known line be 
in the point k. From some point in the line be (such as the point b), 
draw the horizontal line bh and the vertical line bn. The line from o 
through k intersects the horizontal line from b in the point h. From 
the point h, drop a vertical; this intersects the line ov produced, in the 
point m. From m, draw a horizontal line which intersects the vertical 
line from b. This intersection is at the point n. The line vn forms 



360 MASONRY AND REINFORCED CONCRETE 

part of the required line dg. As a check on the work, the lines zg 
and yd should intersect at some point / on the force R. Another 
check on the work, which the student should make, both as a demon- 
stration of the law and as a proof of the accuracy of his work, is to 
select some other point on the line yz than the point o, and likewise 
some other point on the line be than the point b, and make another 
independent solution of the problem. It will be found that when 
the drawing is accurate, the new position for the point n will also be 
on the line dg. 

In applying the above principle to the mechanics of an arch, 
the force A represents the resultant of all the forces acting on the 
arch on one side of the point v through which the desired equilibrium 
polygon is required to pass; and the force B is the resultant of all the 
forces on the other side of that point. A practical illustration of this 
method will be given later. 

CONSTRUCTIVE FEATURES OF MASONRY ARCHES 

402. Definitions of Terms Pertaining to Arch Masonry. Tht, 
following are definitions of technical terms frequently used in con- 
nection with the subject of arch masonry (see Fig. 218) : 

Abutment — The masonry which supports an arch at either end, 
and which is so designed that it can resist the lateral thrust of an 
arch. 

Arch Sheeting — That portion of an arch which lies between the 
ring stones. 

Backing — Masonry which is placed outside of or above the ex- 
trados, with the sole purpose of furnishing additional weight on that 
portion of the arch; it is always made of an inferior quality of masonry 
and with the joints approximately horizontal. 

Coursing Joint — A joint which runs continuously from one face 
of the arch to the other. 

Crown — The highest part of an arch ring. 

Extrados — The upper or outer surfaces of the voussoirs which 
compose the arch ring. 

Haunch — That portion of an arch which is between the crown 
and the skewback; although there is no definite limitation, the term 



MASONRY AND REINFORCED CONCRETE 



361 



applies generally to that portion of the arch ring which is approxi- 
mately half-way between the crown and the skewback. 

Heading Joint — A joint between two consecutive stones in any 
string course. In order that the arch shall be properly bonded to- 
gether, such joints are purposely made not continuous. 

Intrados — The inner or lower surface of an arch. The term is 
frequently restricted to the line which is the intersection of the inner 
surface by a plane which is perpendicular to the axis of the arch. 

Keystone — The voussoir which is placed at the crown of an 
arch. 

Parapet — The wall which is usually built above the spandrel 
walls and above the level of the roadway. 

Rise — The vertical height of the bottom of the keystone above 
the plane of the skewbacks. 



Parapet 



Jpandrel Wall 




Fig. 218. Parts of a Typical Arch. 

Ring Stones — The voussoirs which form the arch ring at each end 
of the arch. 

Skewbacks — The top course of stones on the abutments. The 
upper surfaces of the stones are cut at such an angle that the surfaces 
are approximately perpendicular to the direction of the thrust of the 
arch. 

Soffit — The inner or lower surface of an arch. 

Span — The perpendicular distance between the two springing 
lines of an arch. 

Spandrel — The space between the extrados of an arch and the 
roadway. The walls above the ring stones at the ends of the arch, are 



362 MASONRY AND REINFORCED CONCRETE 

called spandrel walls. The material deposited between the spandrel 
walls and in this spandrel space, is called the spandrel filling. 

Springer — The first arch stone above a skewback. 

Springing Line — The upper (and inner) edge of the line of skew- 
backs on an abutment. 

String Course — A course of voussoirs of the same width (per- 
pendicular to the axis of the arch), which extends from one arch face 
to the other. 

Voussoirs — The separate stones forming an arch ring. 

KINDS OF ARCHES 

403. Arches are variously described according to the shape of 
the intrados, and also according to the form of the soffit : 

Basket-Handled Arch — One whose intrados consists of a series of 
circular arcs tangent to each other. They are usually three-centered 
or five-centered, as described below. 

Catenarian Arch — One whose intrados is the mathematical curve 
known as a catenary. 

Circular Arch — One whose intrados is the arc of a circle. 

Elliptical Arch — One whose intrados is a portion of an el- 
lipse. 

Hydrostatic Arch — One whose intrados is of such a form that the 
equilibrium of the arch is dependent upon such a loading as would be 
made by water. 

Pointed Arch— One whose intrados consists of two similar curves 
which meet at a point at the top of the arch. 

Relieving Arch — An arch which is built above a lintel, which 
relieves the lintel of the greater portion of its load. 

Right Arch — An arch whose soffit is a cylinder, and whose ends 
are perpendicular to the axis of the arch. 

Segmental Arch — One whose intrados is a circular arc which is 
less than a semicircle. 

Semicircular Arch — One whose intrados is a full semicircle. 
Such an arch is also called a full-centered arch. 

Skew Arch — An arch whose soffit may or may not be cylindrical, 
but whose ends are not perpendicular to the axis of the arch. They 
are also called oblique arches. 



MASONRY AND REINFORCED CONCRETE 



363 





VOUSSOIR ARCHES 

404. Definition. A voussoir arch is an arch composed of 
separate stones, called voussoirs, which are so shaped and designed 
that the line of pressures between the stones is approximately per- 
pendicular to the joints between the stones. So far as it affects the 
mechanics of the problem, it is assumed that the mortar in the joints 
between the voussoirs acts merely as a cushion, and that the mortar 
has no tensile strength whatever, even if the pressure at any joint 
should be such as to develop tensile action. It is this feature which 
constitutes the distinction between a voussoir arch and an elastic arch, 
which is assumed to be an arch of 
such material that tensile or trans- 
verse stresses may be developed. 

405. Distribution of the Pres= 
sure between Two Voussoirs. The 
unit-pressure on any joint is as- 
sumed to vary in accordance with 
the location of the center of pres- 
sure, as is illustrated in Fig. 219. 
In the first case, where the center 
of pressure is over the center of 
the face of the joint and is per- 
pendicular to it, the pressure will 
be uniformly distributed, and may 
be represented, as in Fig. 219a, by 
a series of arrows which are all 
made equal, thus representing 
equal unit-pressures. As the center of pressure varies from the center of 
the joint, the unit-pressure on one side increases and the unit-pressure 
on the other side decreases, as shown in Fig. 219 b. The trapezoid in 
this diagram has the same area as the rectangle of the first diagram 
(a), and the center of pressure passes through the center of gravity 
of the trapezoid. As the center of pressure continues to move away 
from the center of the joint, the unit-pressure on one side becomes 
greater, and on the other side less, until the center of pressure is at a 
point J of the width of the joint away from the center. In this case 
(c),the center of pressure is at the extreme edge of the middle third of 





Fig. 219. Distribution of Pressure 



364 MASONRY AND REINFORCED CONCRETE 

the joint. The group of pressures illustrated in diagram c becomes 
a triangle, which means that the pressure at one side of the joint has 
become just equal to zero, and that the maximum pressure at the 
other side of the joint is twice the average pressure. If the line of 
pressure varies still further from the center of the joint, the diagram 
of pressures will always be a triangle whose base is always three times 
the distance of the center of pressure from the nearest edge of the joint. 
If the total pressure on that joint remains constant, then the intensity 
of pressure on one side of the joint becomes extreme, and may be 
sufficient to crush the stone. Also, since the elasticity of the stone 
(or of the mortar between the stones) will cause the stone (or mortar) 
to yield, the yielding being proportional to the pressure, the joint 
will open at the other side, where there is no pressure. In accord- 
ance with this principle of the distribution of pressure, it is always 
specified that a design for an arch cannot be considered safe unless 
it is possible to draw a line of pressure (an equilibrium polygon) 
which shall at every joint pass through the middle third of that joint. 
If the line of pressure at any joint does not pass through the middle 
third, it means that such a joint will inevitably open, and make a bad 
appearance, even though the unit-pressure on the other* end of that 
joint is not so great that the masonry is actually crushed. 

Since the actual crushing strength of stone is a rather uncertain 
and variable quantity, a larger factor of safety is usually employed 
with stone than with other materials of construction. This factor 
is usually made tew; -and therefore, whenever the line of pressures 
passes through the edge of the middle third, the average unit-pressure 
on the joint should not be greater than 2V of the crushing strength of 
the stone. 

A table of these ultimate values has been given in Table I, Part I 
(page 10). They vary from about 3,000 pounds per square inch, 
for a sandstone found in Colorado, up to 28,000 pounds per square 
inch for a granite found in Minnesota. The weaker stone would hard- 
ly be selected for any important work. Usually a stone whose ulti- 
mate strength is 10,000 pounds per square inch or more, would be 
selected for a stone arch. Such a stone could be used with a working 
pressure of 500 pounds per square inch at any joint, assuming that 
the line of pressure does not pass outside of the middle third at any 
joint. 



MASONRY AND REINFORCED CONCRETE 365 

406. External Forces Acting on an Arch. There is always 
some uncertainty regarding the actual external forces acting on 
ordinary arches. The ordinary stone arch consists of a series of 
voussoirs, which are overlaid usually with a mass of earth or cinders 
having a depth of perhaps several feet, on top of which may be the 
pavement of a roadway. The spandrel walls over the ends of the 
arch, especially when made of squared stone masonry, also develop 
an arch action of their own which materially modifies the loading on 
the arch rings. As this, however, invariably assists the arch, rather 
than weakens it, no modification of plan is essential on this account. 
The actual pressure of the earth filling, together with that caused by 
the live load passing over the arch, on any one stone, is uncertain in 
very much the same way as the pressure on a retaining wall is uncer- 
tain, as previously explained. 

The simplest plan is to consider that each voussoir is carrying a 
load of earth equal to that indicated by lines from the joints in the 
voussoir vertically upward to the 

surface. The development of the pavement - i'T load °*£ L^!!^f*?' 

graphical method makes it more r^^^^^f^^P^^^:. 
convenient to draw what is called \y^^ia?tn |/v/^^C^\ 

a reduced load line on top of the S 1" """" ^ 

arch, in which the depth of earth 1 1 I J 

above the arch is reduced in the Fig. 220. Determination of Reduced 

Load Line. 

ratio of the relative weights per 

cubic foot of the earth filling and of the stone of which the 
arch is made (see Fig. 220). Even the live load on the arch 
is represented in the same manner, by an additional area on 
top of the reduced line for the earth pressure, the clepth of that area 
being made in proportion to the intensity of the live load compared 
with the unit-weight of stone. For example, if the earth filling weighs 
100 pounds per cubic foot, and the stone of the arch weighs 160 pounds 
per cubic foot, then each ordinate for the earth load would be yj-jj- of 
the actual depth of the earth. likewise, if the live load per square 
foot on the arch equals 120 pounds, then the area representing the live 
load would be T | % of a foot, according to the scale adopted for the 
arch. The weight of the paving, if there is any, should be similarly 
allowed for. If we draw from the upper end of each joint a vertical 
line extending to the top of the reduced load line, then the area between 



366 



MASONRY AND REINFORCED CONCRETE 



these two verticals and between the arch and the load line represents 
the weight at the scale adopted for the drawing, and at the unit-value 
for the weight per cubic foot (160 pounds per cubic foot, as suggested 
above) actually pressing on that particular voussoir. A line through 
the center of gravity of the stone itself gives the line of action of the 
force of gravity on the voussoir. An approximation to the position 
of this center of gravity, which is usually amply accurate, is the point 
which is midway between the two joints, and which is also on the arch 
curve which lies in the middle of the depth of each voussoir. The 

center of gravity of the load on 
the voussoir is approximately in 
the center of its width. The re- 
sultant of two parallel forces, such 
as V and L, Fig. 221, equals in 
amount their sum R, and its line 
of action is between them and at 
distances from them such that: 
ac : be :: force L: force V. 

Usually the horizontal space 
between the forces V and L is so 
very small that the position of 
their resultant R can be drawn 
by estimation as closely as the 
possible accuracy of drawing will 
permit, without recourse to the 
theoreticallyaccurate method just 
given. The amount of the result- 
ant is determined by measuring 
the areas, and multiplying the 
sum of the two areas by the weight per cubic foot of the 
stone. This gives the weight of a section of the arch ring one 
foot thick (parallel with the axis of the arch). The area of 
the voussoir practically equals the length (between the joints of 
that section) of the middle curve, times the thickness. of the arch ring. 
The area of the load trapezoid equals the horizontal width between 
the vertical sides, times its middle height. The student should 
notice that several of the above statements regarding areas, etc., are not 
theoretically accurate; but, with the usual proportions of the dimen- 




Fig. 221. Graphical Determination of Cir 
eular Arch, Span and Rise Being Known. 



MASONRY AND REINFORCED CONCRETE 367 

sions of the voussoirs to the span of the arch, the errors involved by the 
approximations are harmless, while the additional labor necessary for 
a more accurate solution would not be justified by the inappreciable 
difference in the final results. 

407. Depth of Keystone. The proper depth of keystone for 
an arch should theoretically depend on the total pressure on the key- 
stone of the arch as developed from the force diagram ; and the depth 
should be such that the unit-pressure shall not be greater than a safe 
working load on that stone. But since we cannot compute the stresses 
in the arch, until we know, at least approximately, the dimensions of 
the arch and its thickness, from which we may compute the dead 
weight of the arch, it is necessary to make at least a trial determination 
of the thickness. The mechanics of such an arch may then be com- 
puted, and a correction may subsequently be made, if necessary. 
Usually the only correction which would be made would be to increase 
the thickness of the arch, in case it was found that the unit-pressure 
on any voussoir would become dangerously high. Trautwine's 
Handbook quotes a rule which he declares to be based on a very 
large number of cases that were actually worked out by himself, the 
cases including a very large range of spans and of ratios of span to 
rise. The rule is easily applied, and is sufficiently accurate to obtain 
a trial depth of the keystone. It will probably be seldom, if ever, that 
the depth of the keystone, as determined by this rule, would need to 
be altered. The rule is as follows: 



Depth of Keystone, in feet - V ^o. y alt-sp an + Q 2 ^ (47) 

For architectural reasons, the actual keystone of an arch is 
usually made considerably deeper than the voussoirs on each side of 
it, as illustrated in Fig. 218. When computing the maximum per- 
missible pressure at the crown, the actual depth of the voussoirs on 
each side of the keystone is used as the depth of the keystone; or 
perhaps it would be more accurate to say that the extrados is drawn 
as a regular curve over the keystone (as illustrated in Fig. 223), and 
then any extra depth which may subsequently be given to the key- 
stone should be considered as mere ornamentation and as not af- 
fecting the mechanics of the problem. 

408. Numerical Illustration. The above principles will be 
applied to the case of an arch having a span of 20 feet and a rise of 



368 MASONRY AND REINFORCED CONCRETE 

3 feet (see Fig. 223). If this arch is to be a circular or segmental 
arch, the radius which will fulfil these conditions may be computed 
as illustrated in Fig. 222. We may draw a horizontal -line, at some 
scale, which will represent the span of 20 feet. At the center of 
this line we may erect a perpendicular which shall be 3 feet long 
(at the same scale). Joining the points a and c, and bisecting ac at 
d, we may draw a line from the, bisecting point, which is perpen- 
dicular to ac, and this must pass through the center of the required 

arc. A vertical line through c 
will also pass through the center 
^- "X±- n. of the required arc, and their in- 

tersection will give the point o. 
^ \ I / As a graphical check on the work, 

x \ /a circle drawn about o as a center, 

\ \ / and with oc as a radius, should 

\ \ I ' .also pass through the points a and 

\A I / b. Since some prefer a numerical 

\\ | / / solution to determine the radius 

X 4J_ for a given span and rise, the rad- 

Fig. 222. Resultant Vertical Pressure. ™S f or this Case may be Computed 

as follows : The line ac equals the 
square root of the sum of the squares of the half-span and the 

rise, which equals * ae + ce } but the angle cae = angle aod, and, 
from similar triangles, we may write the proportion : 

ao : ad :: ac : ce. 

ad X ac 1 ac 2 1 ae + ce 1 half-span 2 + rise 2 
ao = 



2 ce 2 ce 2 



This equals numerically in the above case, 109 -r- 6 = 18.17. 

Applying the above rule for the depth of the keystone, we would 
find for this case that the depth should be: 



Depth _ ^L±1±1<L + 0.2 

= S f + 0.2 
4 

= 1.33 + 0.2 

= 1.53 feet. 



Since the total pressure on the voussoirs is always greater at the abut- 
ment than at the crown, the depth of the stones near the end of the 



MASONRY AND REINFORCED CONCRETE 369 

arch should be somewhat greater than the depth of the keystone. We 
shall therefore adopt, in this case, the dimensions of 18 inches for the 
depth of the keystone, and 2 feet for the depth at the skewback. 

409. Plotting the Reduced Load Line. We shall assume that 
the earth or cinder fill on top of the arch has a thickness of one foot at 
the crown, and that it is level on top. We shall also assume that the 
arch ring is composed of stones which weigh 160 pounds per cubic 
foot, and we shall therefore consider 160 pounds per cubic foot as the 
unit-weight in determining the reduced load line. From the ex- 
tremities of the extrados, draw verticals until they intersect the upper 
line of the earth fill. For convenience we shall divide the horizontal 
distance between these verticals into 11 equal parts, each to be about 
2 feet wide. Draw verticals through these points of division down to 
the extrados; then draw radial lines from the extrados to the intrados. 
These lines are drawn radially from a point approximately half- 
way between the center of the extrados and the center of the intrados. 
This means that the joints, instead of being exactly perpendicular to 
either the extrados or intrados, have a direction which is a com- 
promise between the two. The discrepancy is greatest at the abut- 
ments, and approaches zero at the crown. This will divide the arch 
ring into 11 voussoirs, together with a keystone at the center or crown. 
Assuming that the earth fill weighs 100 pounds per cubic foot, the lines 
of division between the 11 sections of the earth fill should each be 
reduced to -J-g-g- or f of its actual depth. If we further assume that 
the pavement is a little over six inches thick, and that its weight is 
equivalent to six inches of solid stone, we may add a uniform ordinate 
equal to six inches in thickness (according to the scale adopted), and 
this gives the total dead load on the arch. We shall assume further a 
live load amounting to 200 pounds per square foot over the whole 
bridge. This is equivalent to -f-jj-J of a foot, or 1 foot 3 inches, of 
solid masonry over the whole arch. This gives the reduced load line 
for the condition of loading that the entire arch is loaded with its 
maximum load. 

As another condition of loading, we shall assume that the above 
load extends only across one-half of the arch. We shall probably 
find that, owing to the eccentricity of this form of loading, the stability 
of the arch is in much greater danger than when the entire arch is 
loaded with a maximum load. 



370 MASONRY AND REINFORCED CONCRETE 

We shall also consider the condition which would be found by 
running a twenty-ton road roller over the arch. A complete test of 
all the possible stresses which might be produced under this condition 
would be long and tedious; but we may make a first trial of it by 
finding the stresses which would be produced by placing the road 
roller at one of the quarter-points of the arch — a position which would 
test the arch almost, if not quite, as severely as any other possible 
position. Owing to the very considerable thickness of earth fill, as 
well as the effect of the pavement, the load of the roller is distributed 
in a very much unknown and very uncertain fashion over a con- 
siderable area of the haunch of the arch. The extreme width of such 
a roller is eight feet; the weight on each of the rear wheels is approxi- 
mately 12,000 pounds. We shall assume that the weight of each 
rear wheel is distributed over a width of three feet and a length of four 
feet, so that the load on the top of the arch under one of the wheels 
may be considered at the rate of 1,000 pounds per square foot over 
an area of 12 square feet. For the unit-section of the arch one foot 
wide, this means a load of 4,000 pounds loaded on two voussoirs 
which are four feet in total length. The front roller of the road roller 
comes between the two rear rollers, and therefore would affect but 
little, if any, the particular arch ring which we are testing. Not only 
is it improbable that there would be a full loading of the arch simul- 
taneously with that of a road roller, but it is also true that a full 
loading would add to the stability of the arch. Yet, in order to make 
the worst possible condition, we shall assume that the part of the arch 
which has the road roller is also loaded for the remainder of its length 
with a maximum load of 200 pounds per square foot; this item alone 
will take care of the effect of the front roller. A load of 1,000 pounds 
per square foot is the equivalent of a loading of 6 feet 3 inches of stone ; 
and therefore, if we draw over voussoirs Nos. 3 and 4 a parallelo- 
gram having a vertical height above the dead-load line equal to 6 feet 
3 inches of stone, and consider a reduced live-load line 15 inches deep 
( I o o = i 25 = 1 foot 3 inches) over the remainder of that half-span, 
we have the reduced load line for the third condition of loading. 

The loads on each voussoir are scaled from the reduced load line 
according to the various conditions of loading. The area between the 
two verticals over each voussoir is measured with all necessary ac- 
curacy by multiplying the horizontal width between the verticals by 



MASONRY AND REINFORCED CONCRETE 



371 



the scaled length of the perpendicular which is midway between the 
verticals. The weight of the voussoir itself may be computed as 
accurately as necessary, by multiplying the radial thickness by the 
length between the joints as measured on the curve lying half-way 
between the intrados and the extrados. 

For example, the load for full loading of the arch which is over 
voussoir No. 1, is measured as follows: The width between the per- 
pendiculars is 2.0 feet; the height measured on the middle vertical is 
4.05 feet;, the area is therefore 8.10 feet, which, multiplied by 160, 
equals 1,296 pounds, which is the load on this voussoir for every foot 
of width of the arch parallel with the axis. The radial thickness of 
voussoir No. 1 is 1.90 feet, and the length is 2.15 feet; this gives an 
area of 4.085 feet, which, multiplied by 160, equals 653.6 pounds. 
The weight of the voussoir is therefore almost exactly one-half that 
of the live and dead loads above it; therefore the resultant of these 
two weights will be almost precisely one-third of the distance between 
the center of this stone and the vertical through the center of the load- 
ing. By drawing this line, we have the line of action of the resultant 
of these two forces, and this value is the sum of 1,296 and 654, or 
1,950 pounds. 

In order to simplify the figure, the arrows representing the lines 
of force of the loading on the voussoir and the weight of the voussoir 
have been omitted from the figure, and only their resultant is drawn in. 
It was of course necessary to draw in these forces in pencil and obtain 
the position of the resultant, as explained in Fig. 221; and then, for 
simplicity, only the resultant was inked in. 

The loads on the other voussoirs are computed similarly. The 
numerical values for the loads on the various voussoirs (including the 
weights of the voussoirs), are tabulated as follows: 

FIRST CONDITION OF LOADING 



Voussoir No. 


Load 


Weight of Voussoir 


• Total 


1 and 1 1 


] ,290 


G54 


1,950 


2 " 10 


1,135 


592 


1,727 


3 " 9 


1,010 


528 


1,538 


4 " 8 


927 


483 


1,410 


5 " 7 


880 


456 


1,336 


6 


867 • 


455 


1,322 



372 



MASONRY AND REINFORCED CONCRETE 



For this first condition of loading, the total loads for voussoirs Nos. 7, 8, 9, 
10, and 11 will be the same as those for voussoirs 5, 4, 3, 2, and 1 respectively. 

The loads for the second condition of loading are found by using 
the same load on the first five voussoirs, but with only half of the live 
load on voussoir No. 6, which means that the load for the first con- 
dition of loading (1,322 pounds) is reduced by 200 pounds, making it 
1,122 pounds. Voussoirs Nos. 7 to 11 are each reduced by 400 pounds. 
The total load for each voussoir is as tabulated below. 

The loads for the third condition of loading are found by using 
the same loads as were employed for the second condition, except that 
for voussoirs Nos. 3 and 4, 1,600 pounds should be added to each 
load. These loads are also tabulated below: 



SECOND CONDITION OF 
LOADING 



THIRD CONDITION OF 
LOADING 



Voussoir No. 


Total Load 


Voussoir No. 


Total Load 


1 


1,950 


1 


1,950 


2 


1,727 


2 


1,727 


3 


1,538 


3 


3,138 


4 


1,410 


4 


3,010 


5 


1,336 


5 


1,336 


6 


1,122 


6 


1,122 . 


7 


936 


7 


936 


8 


1,010 


8 


1,010 


9 


1,138 


9 


1,138 


10 


1,327 


10 


1,327 


11 


1,550 


11 


1,550 



Fig. 223 was originally drawn at the scale of § inch = 1 foot, and 
with the force diagram at the scale of 1,500 pounds per inch. The 
photographic reproduction has of course changed these scales some- 
what. The student should redraw the figure at these scales, and 
should obtain substantially the same final results. 

410. Drawing the Load Line for the First Condition of Loading. 
When the load is uniformly distributed over the entire arch, the load is 
symmetrical, and we need to consider only one-half of the arch. The 
sections of the load line for the force diagram corresponding to this 
condition of loading, must be drawn as explained in detail in Article 397. 
Since the arch is quite flat, the loading is considered to be entirely 
vertical. Since the load is symmetrical and the abutments are at the 



MASONRY AND REINFORCED CONCRETE 



373 



same elevation, we need only draw a horizontal line from the lower 
end of the /ia//-load line, and select on it a trial position (oj for the 
pole, drawing the rays as previously explained; the trial equilibrium 
polygon passes through the center vertical at the point a'. Drawing 
a horizontal line from a' until it intersects the first line (produced) of 
the trial equilibrium polygon, and drawing through it a vertical line, 
we have the line of action of the resultant (R t ) of all the forces on that 
half of the arch. If we draw through a, the center of the keystone, a 
horizontal line, its intersection with R t gives a point in the first line 
(produced) of the true equilibrium polygon. A line from the upper 
end of the load line parallel to this first section of the true equilibrium 



^uc^Loa<f [ Lm^f^^ 



_ 




Fig. 223. Stresses in a 20-Foot Arch. 
Reproduced from an original drawn at scale of J inch = 1 foot. 



polygon, intersects the horizontal line through the middle of the load 
line at o/, which is the position of the true pole. Drawing the rays 
from the true pole to the load line, and drawing the segments of the 
true equilibrium polygon parallel to these rays, we may at once test 
whether the true equilibrium polygon always passes through the 
middle third of each joint. As is almost invariably the case, it is 
found that for full loading, the true equilibrium polygon passes within 
the middle third at every joint. 



374 MASONRY AND REINFORCED CONCRETE 

The student should carefully check over all these calcula- 
tions, drawing the arch at the scale of one-half inch to the foot, and 
the load line of the force diagram at the scale of 1,500 pounds per 
inch; then the rajs of the true equilibrium polygon will represent at 
that scale the pressure at the joints. Dividing the total depth of any 
joint by the pressure found at that joint, gives the average pressure. 
In the case of the joint at the crown, the total pressure at the joint is 
13,900 pounds. The depth of the joint is 1.5 feet, and the area of the 
joint is 216 square inches; therefore the average unit-pressure is 64 
pounds per square inch; if it is assumed that the line of pressure 
passes through either edge of the middle third, then the pressure at 
the edge of the joint is twice the average, or is 128 pounds per square 
inch. This is a very low pressure for any good quality of building 
stone. 

Similarly, the maximum pressure at the skewback is scaled from 
the force diagram as 16,350 pounds; but since the arch is here 
two feet thick, and the area is 288 square inches, it gives an average 
pressure of 57 pounds per square inch. Since this equilibrium 
polygon is supposed to start from the center of this joint, this repre- 
sents the actual pressure. 

Usually it is only a matter of form to make the test for uniform 
full loading. Eccentric loading nearly always tests an arch more 
severely than uniform loading. The ability to carry a full uniform 
load is no indication of ability to carry a partial eccentric loading, 
except that if the arch appeared to be only just able to carry the uni- 
form load, it might be predicted that it would probably fail under the 
eccentric load. On the other hand, if an arch will safely carry a 
heavy eccentric load, it will certainly carry a load of the same in- 
tensity uniformly distributed over it. 

411. Test for the Second Condition, or Loading of Maximum 
Load over One=Half of the Arch. Since the arch has a dead load over 
the entire arch, and a live load over only one-half of the arch, the load 
line for the entire arch must be drawn. The load line for the loaded 
half of the arch will be identical with that already drawn for the 
previous case. The load line for the remainder of the arch may be 
similarly, drawn. This case is worked out by precisely the same 
general method as that already employed in the similar case given 
in detail in Article 410. As in that article, we select a trial pole 



MASONRY AND REINFORCED CONCRETE 375 

which in general will give an oblique closing line for the equilibrium 
polygon. This closing line must be brought down to the horizontal 
by the method already explained in Article 400; then a second trial 
must be made in order to shift the polygon so that it shall pass through 
the middle third at the crown joint. This line should pass through 
the middle of the crown joint; then the real test is to determine how 
it passes through the haunches of the arch. As in the previous case, 
the total pressure at any joint will be determined by the corresponding 
lines in the force diagram, and the unit-pressure at the joint may be 
determined from the area of the joint and the position of the line of 
force with respect to the center of the joint. Even though a line of 
force passed slightly outside of the middle third, it would not neces- 
sarily mean that the arch will fail, provided that the maximum in- 
tensity of pressure, determined according to the principles enunciated 
in Article 405, does not exceed the safe unit-pressure for the kind of 
stone used. 

An inspection of the force diagram with the pole at o 2 ', shows 
that the rays are all shorter than those of the force diagram for the 
first condition of loading — with pole at o/. This means that the 
actual pressure at any joint is less than for the first case; but since the 
true equilibrium polygon for this case does not pass so near the 
center of the joints as it does for the first condition of loading, the 
intensity of pressure at the edges of the joints may be higher than in 
the first case. However, since the equilibrium polygon for this 
second case is always well within the middle third at every joint, and 
since even twice the average joint pressure for the first case is well 
within the safe allowable pressure on any good building stone, we 
may know that the second condition of loading will be safe, even 
without exactly measuring and computing the maximum intensity of 
pressure produced by this loading. 

412. Test for the Third Condition, Involving Concentrated 
Load. The method of making this test is exactly similar to that 
previously given; but on account of a load eccentrically placed, the 
force diagram will be more distorted than in either of the cases previ- 
ously given, and there is greater danger that the arch will prove to 
be unstable on such a test. An inspection of the equilibrium polygon 
for this case shows that the critical point is the joint between vous- 
soirs Nos. 3 and 4. This is what might be expected, since it is the 



376 MASONRY AND REINFORCED CONCRETE 

joint under the heavy concentrated load. The ray in the force dia- 
gram which is parallel to the section of the equilibrium polygon 
passing through this joint, is the ray which reaches the load line 
between loads 3 and 4. This ray, measured at the scale of 1,500 
pounds per square inch, indicates a pressure of 15,625 pounds on the 
joint. The line of pressure is 4f inches from the upper edge of the 
joint; it is outside of the middle third; and therefore the joint will 
probably open somewhere under this loading. According to the 
theory of the distribution of pressure over a stone joint, the pressure 
will be maximum on the upper edge of this joint, and will be zero at 
three times 4} inches, or 14.25 inches, from the upper edge. The 
area of pressure for a joint 12 inches wide will be 14.25 X 12 = 171 
square inches. Dividing 171 into 15,625, we have an average pres- 
sure of 91 pounds, or a maximum pressure of twice this, or 182 
pounds, per square inch at the edge of the joint. But this is such a 
safe working pressure for such a class of masonry as cut-stone vous- 
soirs, that the arch certainly would not fail, even though the elasticity 
of the stone caused the joint to open slightly at the intrados during 
the passage of the steam roller. 

413. Correcting a Design. The above general method of 
testing an arch consists of first designing the arch, and then testing 
it to see whether it will satisfy all the required conditions. In case 
some condition of loading is found which will cause the line of pres- 
sure to pass outside of the middle third or to introduce an excessive 
unit-pressure in the stones, it is theoretically necessary to begin anew 
with another design, and to make all- the tests again on the basis of a 
new design; but it is usually possible to determine with sufficient 
closeness just what alterations should be made in the design so that 
the modified design will certainly satisfy the required conditions. 
For example, if the line of pressure passes on the upper side of the 
middle third at the haunches of the arch, a thickening of the arch at 
that point until the line of pressure is within the middle third of the 
revised thickness, will usually solve the difficulty. The effect of the 
added weight on the haunch of the arch will be to make the line of 
pressure move upward slightly; but the added thickness can allow 
for this. As another illustration, the unit-pressure, as determined for 
the crown of the arch, might be considerably in excess of a safe pres- 
sure for the arch, and it might indicate a necessity to thicken the arch, 



MASONRY AND REINFORCED CONCRETE 377 

not, only at the center, but also throughout the length of the arch. 

For example, in the above numerical case, although it is probably 
not really necessary to alter the design, the arch might be thickened 
on the haunches, say 3 inches. This would add to the weight on the 
haunches one-fourth of the difference of the weights per cubic foot of 
stone and earth, or J (160 — 100) =■ 15 pounds per square foot. This 
is so utterly insignificant compared with the actual total load of about 
750 pounds per square foot, that its effect on the line of pressure is 
practically inappreciable, although it should be remembered that the 
effect, slight as it is, will be to raise the line of pressure. A thickening 
of 3 inches will leave the line of pressure nearly 7| inches (or say 7 J 
inches, to allow generously for the slight raising of the line of pres- 
sure) from the extrados, while the thickness of the arch is increased 
from 19 inches to 22 inches. But the line of pressure would now be 
within the middle third. 

414. Location of True Equilibrium Polygon. In the above 
demonstration, it is assumed that the true equilibrium polygon will 
pass through the center of each abutment, and also through the 
center of the keystone; and the test then consists in determining 
whether the equilibrium polygon which is drawn through these three 
points will pass within the middle third at every joint, or at least 
whether it will pass through the joints in such a way that the maxi- 
mum intensity of pressure at either edge of the joint shall not be 
greater than a safe working pressure. With any system of forces 
acting on an arch, it is possible to draw an infinite number of equilib- 
rium polygons; and then the question arises, which polygon, among 
the infinite number that can be drawn, represents the true equilibrium 
polygon and will represent the actual line of pressure passing through 
the joints. On the general principle that forces always act along the 
line of least resistance, the pressure acting through any voussoir 
would tend to pass as nearly as possible through the center of the 
voussoir; but since the forces of an equilibrium polygon, which rep- 
resent a combination of lines of pressure, must all act simultaneously, 
it is evident that the line of pressure will pass through the voussoirs 
by a course which will make the summation of the intensity of pres- 
sures at the various joints a minimum. It is not only possible but 
probable that the true equilibrium polygon does not pass through the 
center of the keystone, but at some point a little above or below, 



378 MASONRY AND REINFORCED CONCRETE 

through which a polygon may be drawn which will give a less sum- 
mation of pressures than those for a polygon which does pass through 
the point a. The value and safety of the method given above, lie 
in the fact that the true equilibrium polygon always passes through 
the voussoirs in such a way that the summation of the intensities of 
the pressures is the least possible combination of pressures; and 
therefore any polygon which can be drawn through the voussoirs in 
such a way that the pressures at all the joints are safe, merely indicates 
that the arch will be safe, since the true combination of pressures is 
something less than that determined. In other words, the true 
system of pressures is never greater, and is probably less, than the 
system as determined by the equilibrium polygon which is assumed to 
be the true polygon. 

When an equilibrium polygon for eccentric loading passes 
through the arch at some distance from the center of the joint at one 
part of the arch, and very near the center of the joint in all other 
sections, it can be safely counted on, that the true polygon passes a 
little nearer the center at the most unfavorable portion, and a little 
further away from the center at some other joints where there is a 
larger margin of safety. For example, the true equilibrium polygon 
for the third condition of loading (see Fig. 223) probably passes a 
little nearer the center on the left-hand haunch, and a little farther 
away from the center on the right-hand haunch, where there is a 
larger margin; in other words, the whole equilibrium polygon is 
slightly lowered throughout the arch. No definite reliance should be 
placed on this allowance of safety; but it is advantageous to know 
that the margin exists, even though the margin is very small. The 
margin, of course, would reduce to zero in case the equilibrium 
polygon chosen actually represented the true equilibrium polygon. 
While it would be convenient and very satisfactory to be able to obtain 
always the true equilibrium polygon, it is sufficient for the purpose to 
obtain a polygon which indicates a safe condition when we know 
tii;it the true polygon is still safer. 

415. Design of Abutments. The force diagram of Fig. 223, 
which shows the pressures between the voussoirs of the arch, also 
gives, for any condition of loading, the pressure of the last voussoir 
against the abutment. A glance at the diagram shows that the maxi- 
mum pressure against the abutment comes against the left-hand 



MASONRY AND REINFORCED CONCRETE 379 

abutment under the third condition of loading, when the concen- 
trated load is on the left-hand side of the arch. Although the first 
condition of loading does not create so great a pressure against the 
left-hand abutment, yet the angle of the line of pressure is somewhat 
flatter, and this causes the resultant pressure on the base of the abut- 
ment to be slightly nearer the rear toe of the abutment. It is therefore 
necessary to consider this case, as well as that of the third condition 
of loading. 

An abutment may fail in three ways : (1) by sliding on its founda- 
tions; (2) by tipping over; and (3) by crushing the masonry. The 
possibility of failure by crushing the masonry at the skewback may 
be promptly dismissed, provided the quality of the masonry is reason- 
ably good, since the abutment is always made somewhat larger than 
the arch ring, and the unit-pressure is therefore less. The possi- 
bility of failure by the crushing of the masonry at the base, owing to 
an intensity of pressure near the rear toe of the abutment, will be dis- 
cussed below. The possibility that the abutment may slide on its 
foundations is usually so remote that it hardly need be considered. 
The resultant pressure of the abutment on its subsoil is usually nearer 
to the perpendicular than the angle of friction; and in such a case, 
there will be no danger of sliding, even if there is no backing of 
earth behind the abutment, such as is almost invariably found. 

The test for possible tipping over or crushing of the masonry 
due to an intensity of pressure near the rear toe, must be investigated 
by determining the resultant pressure on the subsoil of the abutment. 
This is done graphically by the method illustrated in Fig. 224. This 
is an extension of the arch problem already considered. The line be 
gives the angle of the skewback at the abutment, while the lines of 
,force for the pressures induced by the first and third conditions of 
loading have been drawn at their proper angle. In common with the 
general method used in designing an arch, it is necessary to design 
first an abutment which is assumed to fulfil the conditions, and then 
to test the design to see whether it is actually suitable. The cross- 
section abede has been assumed as the cross-section of solid masonry 
for the abutment. The problem therefore consists in finding the 
amount and line of action of the force representing the weight of the 
abutment. It will be proved that this force passes through the point 
o 5 , and it therefore intersects the pressure on the abutment for the first 



380 



MASONRY AND REINFORCED CONCRETE 



condition of loading, at the point k. The weight of a section of the 
abutment one foot thick (parallel with the axis of the arch), is computed 
(as detailed below) to weigh 19,500 pounds, while the pressure of the 
arch is scaled from Fig. 223 as 16,350 pounds. Laying off these 
forces on these two lines at the scale of 5,000 pounds per inch, we have 
the resultant, which intersects the base at the point m, and which 
scales 31,350 pounds. Similarly, the resultant of the weight of the 
abutment and the line of pressure for the third condition of loading 
intersects the base at the point n, and scales 33,600 pounds. These 

pressures on the 
base will be dis- 
cussed later. 

The line of action 
and the amount of 
the weight of a unit- 
section of the abut- 
ment, are deter- 
mined as follows: 
The center of grav- 
ity of the pentagon 
abode is determined 
by dividing the pen- 
tagon into three ele- 
mentary triangles, 
abe,bce, and cde. We 
may consider be as 
a base which is com- 
mon to the triangles 
abe and bee. By bi- 
secting the base be and drawing lines to the vertices a and c, and tri- 
secting these lines to the vertices, we determine the points o x and o 2 , 
which are the centers of gravity, respectively, of the two triangles. The 
center of gravity of the combination of the two triangles must lie on 
the line joining o t and o 2 , and must be located on the line at distances 
from each end which are inversely proportional to the areas of the tri- 
angles. Since the triangles have a common base be, their areas are nro- 
portional to their altitudes af and (je. In the diagram at the side, ITS; 
may lay off in succession, on the horizontal line, the distances gc and af. 




Fig. 2li. Forces Acting on Abutments. 



MASONRY AND REINFORCED CONCRETE 381 

On the vertical line, we lay off a distance equal to o x o 2 . By joining the 
lower end of this line with the right-hand end of the line aj, and then 
drawing a parallel line from the point between gc and af, we have 
divided the distance o x o 2 into two parts which are proportional to the 
two altitudes af and gc. Laying off the shorter of these distances 
toward the triangle abe (since its greater altitude shows that it has 
the greater area), we have the position of o 3 , which is the center of 
gravity of the two triangles combined. The area abce is measured 
by one-half the product of eb and the sum of af and gc. The triangle 
cde is measured by one-half the product of the base ed by the altitude 
ck. If we lay off be as a vertical line in the side diagram, and also the 
line ed as a vertical line, and join the lower end of ed with the line 
which represents the sum of gc and af, and then draw a line from the 
lower end of be, parallel with this other line, we have two similar 
triangles from which we may write the proportion : 

ed : (gc + af) :: be : a'f'g'c' '. 
Since the product of the means equals the product of the extremes, we 
find that (gc + af) X be = ed X a'fg'c'; but \ (gc + af) X be = 
the combined area of the two triangles, and therefore the line a'fg'c' 
is the height of an equivalent triangle whose base equals ed; therefore 
the area of these two combined triangles is to the area of the triangle 
cde as the equivalent altitude a'fg'c' is to the altitude ch of the triangle 
cde. By bisecting the base ed, and drawing a line from the bisecting 
point to the point c, and trisecting this line in the point o 4 , we have 
the center of gravity of the triangle cde. The center of gravity of the 
entire area, therefore, lies on the line o^o^ and at a distance from o 4 
which is inversely proportional to the areas of the two combined 
triangles and the triangle cde. These areas are proportional to the 
altitudes as determined above; therefore, by laying off in the side 
diagram the line o z o v and drawing a line from its lower extremity to 
the right-hand extremity of the line ch, and then drawing a parallel 
line from the point between a'fg'c' and ch, we divide the line o 3 o 4 into 
two parts which are proportional to these altitudes. The line ch is the 
greater altitude, and the triangle cde has the greater area; therefore 
the point o 5 is nearer to the point o 4 than it is to the point o 3 , and the 
shorter of these two sections is laid off from the point o 4 . This gives 
the point o 5 , which is the center of gravity of the entire area of the 
abutment. 



382 MASONRY AND REINFORCED CONCRETE 

The actually computed weight of a unit-section of the abutment 
is determined by multiplying the sum of a'fg'c' and ch by the base ed. 
Since this masonry is assumed to weigh 160 pounds per cubic foot, 
the product of these scaled distances, measured at the scale of J inch 
equals one foot (which was the scale adopted for the original drawing), 
shows that the section one foot thick has a weight of 19,500 pounds. 
Laying off this weight from the point k, and laying off the pressure for 
the first condition of loading, 16,350 pounds, at the scale of 5,000 
pounds per inch, and forming a parallelogram on these two lines, we 
have the resultant of 31,350 pounds as the pressure on the base of the 
abutment, that pressure passing through the point m. 

The intersection of the weight of the abutment with the line of 
pressure for the third condition of loading, is a little below the point 
k; and we similarly form a parallelogram which shows a resulting 
pressure of 33,600 pounds, passing through the base at the point n. 
It is usually required that such a line of pressure shall pass through 
the middle third of the abutment; but there are other conditions 
which may justify the design, even when the line of pressure passes a 
little outside of the middle third. 

The point n is 2.85 feet from the point e. According to the theory 
of pressures enunciated in Article 405, it may be considered that the 
pressure is maximum at the point e, and that it extends backward 
toward the point d for a distance of three times en, or a distance of 
8.55 feet. This would give an average pressure of 3,930 pounds per 
square foot, or, since the pressure at the toe is twice t^e average 
pressure, 7,860 pounds per square foot on the toe. Such a pressure 
might or might not be greater than the subsoil could endure without 
yielding. Since this pressure is equivalent to about 55 pounds per 
square inch, there should be no danger that the masonry itself would 
fail; and, if the subsoil is rock or even a hard, firm clay, there will be 
no danger in trusting such a pressure on it. 

Another very large item of safety which has been utterly ignored, 
but which would unquestionably be present, is the pressure of the 
earth back of the abutment. The effect of the back-pressure of the 
earth would be to make the line which represents the resultant pres- 
sure on the subsoil more nearly vertical, and to make it pass much 
more nearly through the center of the base ed. This would very much 
reduce the intensity of pressure near the point e, and would reduce 



MASONRY AND REINFORCED CONCRETE 383 

very materially the unit-pressure on the subsoil. Cases, of course, 
are conceivable, in which there might be no back-pressure of earth 
against the rear of the abutment. In such cases, the ability of the 
subsoil to withstand the unit-pressure at the rear toe of the abutment 
(near the point e) must be more carefully considered. In order that 
the investigation shall be complete, it should be numerically deter- 
mined whether the lower pressure, 31,350 pounds, passing through 
the point m, might produce a greater intensity of pressure at the point 
e than the larger pressure passing through the point n. 

416. Various Forms of Abutments. The abutment described 
above is the general form which is adopted very frequently. The 
front face cd is made with a batter of one in twelve. The line ha slopes 
backward from the arch on an angle which is practically the con- 
tinuation of the extrados of the arch. The total thickness of the abut- 
ment de must be such that the line of pressure will come nearly, if not 
quite, within the middle third. The line ea generally has a con- 
siderable slope, as is illustrated. When the subsoil is very soft, so 
that the area of the base is necessarily very great, the abutment is 
sometimes made hollow, with the idea of having an abutment with a 
very large area of base, but which does not require the full weight of 
so much masonry to hold it down; and therefore economy is sought 
in the reduction of the amount of masonry. Since such a hollow 
abutment would require a better class of masonry than could be used 
for a solid block of masonry, it is seldom that there is any economy in 
such methods. Since the abutment of an arch invariably must with- 
stand a very great lateral thrust from the arch, there is never any 
danger that the resultant pressure of the abutment on the subsoil 
will approach the front toe of the arch, as is the case in the abutment 
of a steel bridge, which has little or no lateral pressure from the bridge, 
but which is usually subjected to the pressure of the earth behind it. 
These questions have already been taken up under the subject of 
abutments for truss bridges, in Part II. 

VOUSSOIR ARCHES SUBJECTED TO OBLIQUE FORCES 

417. Determination of Load on a Voussoir. The previous 
determinations have been confined to arches which are assumed to 
be acted on solely by vertical forces. For flat segmental arches, or 



384 MASONRY AND REINFORCED CONCRETE 

even for elliptical arches where the arch is very much thickened at 
each end so that the virtual abutment of the arch is at n considerable 
distance above the nominal springing line, such a method is suffi- 
ciently accurate, and it has the advantage of simplicity of computa- 
tion; but where the arch has a very considerable rise in comparison 
with its span, the pressure on the extrados, which is presumably 
perpendicular to the surface of the extrados, has such a large hori- 
zontal component that the horizontal forces cannot be ignored. The 
method of determining the amount and direction of the force acting 
on each voussoir, is illustrated in Fig. 225. The reduced load line, 
found as previously described, is indicated in the figure. A trapezoid 
represents the loading resting on the voussoir ac. The line dj repre- 
sents, at some scale, the amount of this vertical loading. Drawing the 
line de perpendicular to the extrados ac, we may complete the rec- 
tangle on the line df, and obtain the horizontal component, while the 
equivalent normal pressure on the voussoir is represented by de. 

Drawing a vertical line through the center of gravity of the vous- 
soir, and producing it (if necessary) until it intersects ed in the point v, 
we may lay off vw to represent, at the same scale, the weight of the 
voussoir. Making vs equal to de, we find vt as the resultant of the 
forces; and it therefore measures, according to the scale chosen, the 
amount and direction of the resultant of the forces acting on that 
voussoir. Although the figure apparently shows the line de as though 
it passed through the center of gravity of the voussoir, and although it 
generally will do so very nearly, it should be remembered that de does 
not necessarily pass through the center of gravity of the voussoir. 

A practical graphical method of laying off the line vt to represent 
the actual resultant force is as follows: The reduced load line, drawn 
as previously described, gives the line for a loading of solid stone, 
which would be the equivalent of the actual load line. If this loading 
has a unit-value of, say, 160 pounds per cubic foot, and if the horizontal 
distance ah is made 2 feet for the load over each voussoir, then each 
foot of height (at the same scale at which ah represents 2 feet) of the 
line gd represents 320 pounds of loading. If the voussoir were actual- 
ly a rectangle, then its area would be equal to that of the dotted 
parallelogram vertically under ac, and its area would equal ah X dk; 
and in such a case, dk would represent the weight of that voussoir, and 
the force vw could be scaled directly equal to dk, without further compu- 



MASONRY AND REINFORCED CONCRETE 



385 



Reduced 
Load Line 



tation. The accuracy of this method, of course, depends on the 
equality of the dotted triangle below c and that below a. For vous- 
soirs which are near the crown of the arch, the error involved by this 
method is probably within the general accuracy of other determina- 
tions of weight; but near the abutment of 
a full-centered arch, the inaccuracy would 
be too great to be tolerated, and the area of 
the voussoir should be actually computed. 
Dividing the area by 2 (or the width ab), 
we have the equivalent height in the same 
terms at which gd represents the external 
load, and its equivalent height would be 
laid off as viv. 

418. Application to a Definite Prob= 
lem. We shall assume for this case a full- 
centered circular arch whose intrados has 
a radius of 15 feet. The depth of the 
keystone computed according to the rule 
given in Equation 47, would be 1.57 feet, 
which is practically 19 inches. By drawing 
first the intrados of the arch as a full semi- 
circle (see Fig. 226), and then laying off 
the crown thickness of 19 inches, we find 
by trial that a radius of 20 feet, for the 
extrados will make the arch increase to a 
thickness of about 2\ feet at a point 45 
degrees from the center, which is usually a critical point in such arches. 
We shall therefore draw the extrados with a radius of 20 feet, the 
center point being determined by measuring 20 feet down from the 
top of the keystone. We shall likewise assume that this arch is one 
of a series resting on piers which are 4 feet thick at the springing line. 

By drawing a portion of the adjoining arch, we find that its 
extrados intersects the extrados of the arch considered at a point 
about 7 feet 6 inches above the pier. By drawing a line from this 
point toward the center for joints, which is about midway between the 
center for the extrados and the center for the intrados, we have the 
line for the joint which is virtually the skewback joint and the abut- 
ment of the arch. 




Resultant of Oblique 
Pressures. 



386 



MASONRY AND REINFORCED CONCRETE 



The center of the pier is precisely 17 feet from the center of the 
arch. We shall assume that the arch is overlaid with a filling of 
earth or cinders which is 18 inches thick at the crown, and that it is 
level. Drawing a horizontal line to represent the top of this earth 
filling, we may divide this line into sections which are 2 feet wide, 
commencing at the vertical line through the center of the pier. Ex- 
tending this similarly to the other side of the arch, we have eight 
sections of loading on each side of the keystone section. Drawing 
lines from the points where these verticals between the sections inter- 




Fig. 226. Resultant Forces Acting on Voussoirs of a Full-Centered Arch. 

sect the extrados, toward the center for joints, previously determined, 
we have the various joints of the voussoirs. Assuming, as in the 
previous numerical problem that the cinder fill weighs 100 pounds 
per cubic foot, and that the stone weighs 160 pounds per cubic foot, 
we determine the reduced load line for the top of the earth fill over 
the entire arch. 

We shall assume that the arch carries a railroad track and a 
heavv class of traffic. The weight of roadbed and track may be 
computed as follows: The ties are to be 8 feet long; the weight of 



MASONRY AND REINFORCED CONCRETE 387 

the roadbed and track (and also the live load) is assumed to be dis- 
tributed over an area 8 feet wide. 

Two rails at 100 pounds per yard will weigh, per square foot 

of surface 8.4 lbs. 

Oak ties, weighing 150 pounds per tie, will weigh, per square foot 

of surface 9.4 " 

Weight of ballast at 100 pounds per cubic foot, average 

depth 9 inches 75.0 " 

Total weight 92.8 lbs. 

This is the equivalent of 0.58 foot depth of stone, and we therefore 
add this uniform depth to the reduced load line for the earth. 

A 50-ton freight-car, fully loaded, will weigh 134,000 pounds; 
with a length between bumpers of 37 feet, this will exert a pressure of 
about 450 pounds per square foot on a strip 8 feet wide. This is equiv- 
alent to 2.8 feet of masonry. We shall therefore consider this as a 
requirement for uniform loading over the whole arch. 

It would be more precise to consider the actual wheel loads for 
the end trucks of two such cars which are immediatelv following each 
other; but since the effect of this woidd be even less than that of the 
calculation for a locomotive, which will be given later, and since the 
deep cushion of earth filling will largely obliterate the effect of con- 
centrated loads, the method of considering the loading as uniformly 
distributed will be used. We therefore add the uniform ordinate 
equal to 2.8 feet over the whole arch. We shall call this the first 
condition of loading. 

We shall assume for the concentrated loading, a consolidation 
locomotive with 40,000 pounds on each of the four driving axles, spaced 
5 feet apart. This means a wheel base 15 feet long; and we shall 
assume that this extends over voussoirs 1 to 8 inclusive, while the 
loading of 450 pounds per square foot is on the other portion of the 
arch. A weight of 40,000 pounds on an axle, which is supposed to be 
distributed over an area 5 feet long and 8 feet wide, gives a pressure 
of 1,000 pounds per square foot, or it would add an ordinate of 0.33 
feet of stone; these ordinates are added above the load line repre- 
senting the load of the roadbed and track. We shall call this the 
second condition of loading. 

The load for each voussoir is determined by the method given 
in Article 417. The direction of the pressure on the voussoir is 



388 MASONRY AND REINFORCED CONCRETE 

determined by drawing a line toward the extrados center from the 
intersection of the vertical through the trapezoid of loading with the 
extrados. The length of that vertical is laid off below that point of 
intersection; then a horizontal line drawn from the lower end of the 
vertical intersects the line of force at a point which measures the 
amount of that pressure on the voussoir. The area of the voussoir 
is determined as described in Article 417; and the resultant of the 
loading and the weight of the voussoir is obtained. This is indicated 
as force No. 1 in Fig. 226. In this case, it includes the locomotive 
loading on the left-hand side of the arch. The forces acting on 
voussoirs Nos. 2, 3, 4, 5, 6, 7, and 8 are similarly determined. The 
forces on voussoirs Nos. 9 to 17 inclusive, on the basis of the uniformly 
distributed load equal to 450 pounds per square foot, are also similarly 
determined. The loads on voussoirs Nos. 10 to 17 inclusive will be 
considered to measure the loads on voussoirs Nos. 8 to 1 inclusive, 
for the first condition of loading. The loading with the locomotive 
over voussoirs Nos. 1 to 8, and cars over voussoirs Nos. 9 to 17, con- 
stitutes the second condition of loading. 

As described above, the arrows representing the forces in Fig. 
226 are drawn at a scale such that each f of an inch represents 2 cubic 
feet of masonry, or 320 pounds; therefore every inch will represent 
the quotient of 320 divided by |, or 853 pounds per linear inch. The 
practical method of making a scale for this use is illustrated in the 
diagram in the upper right-hand corner of Fig. 226. We may draw 
a horizontal line as a scale line, and lay off on it, with a decimal scale, 
a length ca which represents, at some convenient scale, a length of 
800. Drawing the line ab at any convenient angle, we lay off from 
the point c the length cb to represent 853 at the same scale as that used 
for ca. The line cd is then laid off to represent 7,000 units at the 
scale of 800 units per inch. By drawing a line from d parallel to ba, 
we have the distance ce, which represents 7,000 units at the scale of 
853 units per inch. By trial, a pair of dividers may be so spaced 
that it steps off precisely seven equal parts for the distance ce; or the 
line ce may also be divided into equal parts by laying off on cd to the 
decimal scale, the seven equal parts of 1,000 each which arc at the 
scale of 800 units per inch; and then lines may be drawn from these 
points parallel to ba and de. The last division may be similarly 
divided into 10 equal parts, which will represent 100 pounds each. 



MASONRY AND REINFORCED CONCRETE 



389 



Using dividers, the resultant force on each voussoir from No. 1 to 
No. 17 may be scaled off as follows : 



1 


7,825 


10 


1,910 


2 


5,970 


11 


2,040 


3 


4,940 


12 


2,200 


4 


4,190 


13 


2,400 


5 


3,725 


14 


2,905 


6 


3,380 


15 


3,570 


7 


3,170 


1G 


4,420 


8 


3,040 


17 


6,005 


9 


1,880 







The student should note the three dotted curves in the lower 
part of the figure, which have been drawn through the extremities 
of the forces. The only object in drawing these three curves is 
merely to note the uniformity with which the ends of these arrows 
form a regular curve. If it was found that one of the forces did not 
pass through this curve, it would probably imply a blunder in the 
method of determining that particular force. Even if such curves 
are not actually drawn in, it is well to observe that the points do come 
on a regular curve, as this constitutes one of the checks on the graphi- 
cal solution of problems. 

Fig. 226 is merely the beginning of the problem of determining 
the stresses in the arch. In order to save the complication of the 
figure, the arch itself and the resultant forces (1 to 17) are repeated 
in Fig. 227, the direction, intensity, and point of application of these 
forces being copied from one figure to the other. 

Forces Nos. 1 to 17 are drawn in the force diagram of Fig. 227 
at the scale of 4,000 pounds per inch. Forces 1 to 8, inclusive, have a 
resultant whose direction is given by the line marked R t " which joins 
the extremities of forces 1 to 8. Similarly, the direction of the re- 
sultant (/?/ or R 2 ') of forces 9 to 17, inclusive, is given by the line 
which joins the extremities of this group. The direction of the resul- 
tant of all the forces Nos. 1 to 17, is given by the line joining the ex- 
tremities of these forces in the force diagram, this resultant being 
marked R 2 . By choosing a pole at random (the point o 2 r in the force 
diagram), drawing rays to the forces, and beginning at the left-hand 
abutment, we may draw the trial equilibrium polygon, which passes 



390 



MASONRY AND REINFORCED CONCRETE 



through the point a on force No. 17. The line through a parallel 
to the last ray, has the direction ab. Producing the section of the 
polygon which is between forces 8 and 9 (and which is parallel to 
the ray which reaches the load line between forces 8 and 9), it inter- 
sects the first and last lines of the trial equilibrium polygon at the 
points b and d. The point b is therefore a point on the resultant RJ 
of forces Nos. 9 to 17 inclusive; and by drawing a line parallel to the 
force R 2 ' in the force diagram, we have the actual line of action of the 
resultant. 

Similarly, the line of action of the force i? 9 " is determined by 



ipecial eguil polygon forjecond 
condition of loading 



Scale of force diagram 
*■ fooo pound; per inch 




Fig. 227. Pressures <>u Voussoirs of a Full-Centered Arch. 

drawing from the point d a line parallel to R" in the force diagram. 
Their intersection at the point e gives a point in the line of action of the 
resultant of the whole system of forces, R 2 ; and by drawing from the 
point e a line parallel to R 2 of the force diagram, we have the line of 
action of R r We select a point (/) at random on the resultant R 2 , and 
join the point / with the center of each abutment. By drawing lines 
from the extremities of the load line parallel to these two lines from /, 
they intersect at the point o". A horizontal line through o" is there- 
fore the locus of the pole of the true equilibrium polygon passing 



MASONRY AND REINFORCED CONCRETE 391 

through the center of both abutments. The line fn intersects R 2 in the 
point g, and the line fm intersects the force R 2 in the point h. The 
intersection of gh with the vertical through the center (the point i) is 
the trial point which must be raised up to the point c, which is done 
by the method illustrated in Article 401. The application of this 
method gives the line kl, passing through c; and the line In is there- 
fore the first line of the special equilibrium polygon for the complete 
system of forces from No. 1 to No. 17; and the line km is similarly 
the last line of that polygon. By drawing lines from the extremities 
of the load line, parallel to In and km, we find that they intersect at 
the point o 2 '" , which is the pole of the special equilibrium polygon 
passing through n, c, and m, for the complete system of forces Nos. 1 
to 17. 

As a check on the work, the intersection of these lines from the 
ends of the load line, parallel to In and km, must be on the horizontal 
line passing through o" . By drawing rays from the new pole o'" to 
the load line, and completing the special equilibrium polygon, we 
should find as a double check on the work, that both of these partial 
polygons starting from m and n should pass through the point c; and 
also that the section of the polygon between forces Nos. 8 and 9 lies 
on the line kl. This gives the special equilibrium polygon for 
the system of forces Nos. 1 to 17, which corresponds with the second 
condition of loading, as specified above. 

The first condition of loading is given by duplicating about the 
center, in the force diagram, the system of forces from No. 17 to No. 9 
inclusive. Since this system of forces is symmetrical about the center, 
we know that its resultant R t passes through the center of 
the arch, and that it must be a vertical force. We may draw from 
the middle of force No. 9 a horizontal line, and also draw a vertical 
from the lower end of the load line. Their intersection is evidently 
at the center of the resultant R v which is there fore carried above this 
horizontal line for an equal amount. Joining the upper end of R t 
with the upper end of force No. 9 3 we have the direction and amount 
of the force R". The intersection of ng with the force R x at the point 
j, gives a point which, when joined with the point m, gives one line of 
a trial equilibrium polygon passing through the required points m and 
n, but which does not pass through the required point c. The inter- 
section of j m with the force R" at the point p, gives .us the line pg, 



392 MASONRY AND REINFORCED CONCRETE 

which is the same kind of line for this trial polygon as the line Incj 
was for the other. 

By a similar method to that used before and as described in 
detail in Article 401, we obtain the line qr passing through c, which 
gives us also the section of our true equilibrium polygon between 
forces Nos. 8 and 9. The line rn also gives us that portion of the true 
equilibrium polygon for this system of loading, from the point n up 
to the force No. 17. 

By drawing a line from the lower end of the load line, parallel to 
nr, until it intersects the horizontal line through the middle of force 
No. 9 at the point o/, we have the pole of the special equilibrium 
polygon for this system of loading, which is the first condition of load- 
ing. The rays are drawn from o/ only to the forces from No. 9 to 
No. 17 inclusive, and the special equilibrium polygon is completed 
between n and c by drawing them parallel to these rays. 

On account of the symmetry of loading, we know that the equilib- 
rium polygon would be exactly similar on the left-hand side of the 
arch. In discussing these equilibrium polygons, Ave must therefore 
remember that of the two equilibrium polygons lying between the 
extrados and intrados on the right-hand side of the arch, the upper 
line represents the line of pressure for a uniform loading over the 
whole arch (the first condition of loading), while the lower line on the 
right-hand side, and also the one equilibrium polygon which is shown 
on the left-hand side of the arch, represent the special equilibrium 
polygon for the second condition of loading. 

419. Intensity of Pressures on the Voussoirs of the Arch. An 
inspection of the equilibrium polygon for the first condition of loading, 
shows that it passes everywhere within the middle third. The maxi- 
mum total pressure on a joint, of course, occurs at the abutment, 
where the pressure equals 24,750 pounds. Since the joint is here 
about 42 inches thick, and a section one foot wide has an area of 504 
square inches, the pressure on the joint is at the rate of 49 pounds per 
square inch. At the keystone, the actual pressure is 19,750 pounds; 
and since the keystone has an area of 228 square inches, the pressure 
is at the rate of 87 pounds per square inch. 

At the joint between forces Nos. 13 and 14, the line of force passes 
just inside the edge of the middle third. The ray from the pole o/ 
to the joint between voussoirs Nos. 13 and 14 of the force diagram, 



MASONRY AND REINFORCED CONCRETE 393 

has a scaled length of 20,250 pounds. The joint has a total thickness 
of about 24 inches, and therefore an area of 288 square inches. This 
gives an average pressure of 70 pounds per square inch; but since the 
line of pressure passes near the edge of the middle third, we may 
double it, and say that the maximum pressure at the upper edge of 
the joint is 140 pounds per square inch. All of these pressures for 
the first condition of loading are so small a proportion of the crushing 
strength of any stone such as would be used for an arch, or even of 
the good quality of mortar which would of course be used in such a 
structure, that we may consider the arch as designed, to be perfectly 
safe for the first condition of loading. 

The special equilibrium polygon for the second condition of 
loading shows that the stability of the arch is far more questionable 
under this condition, since the special equilibrium polygon passes out- 
side the middle third, especially on the left-hand haunch of the arch. 
The critical joint appears to be between voussoirs Nos. 4 and 5. The 
pressure at this joint, as determined by scaling the distance from the 
point o 2 r// to the load line between forces Nos. 4 and 5, is approxi- 
mately 24,500 pounds. The section of the equilibrium polygon 
parallel to this ray passes through the joint at a distance of a little 
over three inches from the edge. On the basis of the distribution of 
pressure at a joint, the compression at this joint would be confined to 
a width of 9 inches from the upper edge, the pressure being zero at a 
distance of 9 inches from the edge. This gives an area of pressure 
of 108 square inches, and an average pressure of 227 pounds per 
square inch. At the upper edge of the joint, there would therefore be 
a pressure of double this, or 454 pounds per square inch. This 
pressure approaches the extreme limit of intensity of pressure which 
should be used in arch work ; and even this should not be used unless 
the voussoirs were cut and dressed in a strictly first-class manner, and 
the joints were laid with a first-class quality of mortar. 

The propriety of leaving the dimensions as first assumed for trial 
figures, depends, therefore, on the following considerations: 

First — The loading assumed above for the uniformly distributed 
load is as great a loading as that produced by ordinary locomotives 
such as are used on the majority of railroads; while the locomotive 
requirements as assumed above are excessive, and are used on only 
a comparatively few railroads. 



394 MASONRY AND REINFORCED CONCRETE 



Second — If an equilibrium polygon had been started from a 
point nearer the intrados than the point m (using the same pole o/"), 
it would have passed a little below the point c, and likewise a little 
nearer the intrados than the point n. Although this would have 
brought the equilibrium polygon a little nearer to the intrados on the 
right-hand haunch of the arch, it would likewise have drawn it away 
from the extrados on the left-hand haunch, Although it is uncertain 
just which equilibrium polygon, among the infinite number which 
may mathematically be drawn, will actually represent the true equilib- 
rium polygon, there is reason to believe that the true equilibrium 
polygon is the one of which the summation of the intensity of pres- 
sures at the various joints is a minimum; and it is evident from mere 
inspection, that an equilibrium polygon drawn a little nearer the 
center (as described above) will have a slightly less summation of 
intensity of pressure, although the intensity of pressure on the joints 
on the right-hand haunch will rapidly increase as the polygon ap- 
proaches the intrados. It is therefore quite possible that the true 
equilibrium polygon would have a less intensity of pressure at the 
joint between voussoirs Nos. 4 and 5. 

If it is still desired to increase the thickness of the arch so that 
the line of pressure will pass further from the extrados, it may be done 
approximately as indicated for a similar problem in Article 414. 
Evidently the keystone is sufficiently thick, and the voussoirs at the 
abutments also have ample thickness. The extrados must evidently 
be changed from an arc of a circle to some form of curve which shall 
pass through the same three points at the crown and the two abut- 
ments. This may be either an ellipse or a three-centered or five- 
centered curve. Although it will cause an extra loading on the 
haunches of the arch to increase the thickness of the arch on the 
haunches, and although this will cause the equilibrium polygon to 
rise somewhat, the rise of the equilibrium polygon will not be nearly 
so rapid as the increase in the thickness of the arch; and therefore the 
added thickness will add very nearly that same amount to the distance 
from the extrados to the equilibrium polygon. For example, by 
adding a little over three inches to the thickness of the arch at vous- 
soirs Nos. 4 and 5, the distance from the equilibrium polygon to the 
extrados would be increased from three inches to six inches, and the 
maximum intensity of pressure on the joint would be approximately 



MASONRY AND REINFORCED CONCRETE 395 



half of the previous figure. To be perfectly sure of the results, of 
course, the problem should be again worked out on the basis of the 
new dimensions for the arch. 

The required radii for a multi-centered arch which should have 
this required extrados, or the axes of an arc of an ellipse which should 
pass through the required points, are best determined by trial. The 
effect of the added thickness on the load line for the right-hand side 
of the arch, will be to bring the load line nearer to the center of the 
voussoirs, and therefore will actually improve the conditions on that 
side of the arch. Of course, when the concentrated load is over the 
right-hand side -of the arch instead of the left, the form of the equilib- 
rium polygon will be exactly reversed. It is quite probable that, 
for mere considerations of architectural effect, the revised extrados 
would be made the same kind of a curve as the intrados. This would 
practically be done by selecting a radius which would leave the same 
thickness at the crown, allow the required thickness on the haunches, 
and let the thickness come what it will at the abutments, even though 
it is needlessly thick. 

420. Stability of the Pier between the Arches. The stability 
of the pier on the right-hand side of the arch in Fig. 227, is deter- 
mined on the assumption of the concentrated locomotive loading on 
the left-hand end of the next arch which is at the right of the given 
arch, and the uniform loading over the right-hand end of the given 
arch. We therefore draw through the point m f a line of force parallel 
to mk, and also produce the line In until it intersects the other line 
of force in the point s. A line from s parallel to R 2 , therefore, gives 
the line of action of the resultant of the forces passing down the pier, 
for this system of loading. Since this system of loading will give 
the most unfavorable condition, or the condition which will give a 
resultant with the greatest variation from the perpendicular, we shall 
consider this as the criterion for the stability of the pier. The piers 
were drawn with a batter of 1 in 12, and it should be noted that the 
resultant R 2 is practically parallel to the batter line. If the slope of 
R 2 were greater than it is, the batter should then be increased. The 
value of R 2 is scaled from the force diagram as 55,650 pounds. The 
force R 2 is about 14 inches from the face of the pier, and this would 
indicate a maximum intensity of pressure of 221 pounds per square 
inch. This is a safe pressure for a good class of masonry work. The 



396 MASONRY AND REINFORCED CONCRETE 

actual pressure on the top of the pier is somewhat in excess of this, 
on account of the weight of that portion of the arch between the virtual 
abutment at n and the top of the pier; and the total pressure at any 
lower horizontal section, of course, gradually increases; but on the 
other hand, the weight of the pier combines with the resultant thrust 
of the two arches to form a resultant which is more nearly vertical 
than R 2 , and the center of pressure therefore approaches more nearly 
to the axis of the pier. The effect of this is to reduce the intensity of 
pressure on the outer edge of the pier; and since the numerical result 
obtained above is a safe value, the actual maximum intensity of 
pressure is certainly safe. 

ELASTIC ARCHES 

421. Technical Meaning. All of the previous demonstrations 
in arches have been made on the basis that the arch is made up of 
voussoirs, which are acted on only by compressive forces. The 
demonstration would still remain the same, even if the arches were 
monolithic rather than composed of voussoirs; but in the case of an 
arch composed of voussoirs, it is essential that the line of pressure 
shall pass within the middle third of each joint, in order to avoid a 
tendency for the joint to open. If the line of pressure passes very far 
outside of the middle third of the joint, the arch will certainly collapse. 
An elastic arch is one which is capable of withstanding tension, which 
practically means that the line of pressure may pass outside of the 
middle third and even outside of the arch rib itself. In such a case, 
transverse stresses will be developed in the arch at such a section, and 
the stability of the arch will depend upon the ability of the arch rib 
to withstand the transverse stresses developed at that section. A 
voussoir arch is, of course, incapable of withstanding any such 
stresses. A monolithic arch of plain concrete could withstand a con- 
siderable variation of the line of pressure from the middle third of 
the arch rib; but since its tensile strength is comparatively low, this 
variation is very small compared with the variation that would be 
possible with a steel arch rib. A reinforced-concrete arch rib can be 
designed to stand a very considerable variation of the line of pressure 
from the center of the arch rib. 

422. Advantages and Economy. The durability of concrete, 
and the perfect protection that it affords to the reinforcing steel which 



MASONRY AND REINFORCED CONCRETE 397 



is buried in it, give a great advantage to these materials in the con- 
struction of arch ribs. Although the theoretical economy is not so 
great as might be expected, there are some very practical features 
which render the method economical. It is always found that, before 
any considerable transverse stresses can be developed in a reinforced- 
concrete arch bridge, the concrete will be compressed to the maximum 
safe limit while the unit-stress in the steel is still comparatively low. 
Since a variation in the dead load often changes the line of pressure 
from one side of the arch rib to the other, and thus changes the 
direction of the transverse bending, it becomes necessary to place 
steel near both faces of the arch rib, in order to withstand the tension 
which will be alternately on either side of the rib. Of course the steel 
which is (for the moment) on the compressive side of the rib will assist 
the concrete in withstanding compression, but this is not an economi- 
cal use of the steel. There is, however, the practical economy and 
advantage, that the reinforcement of the concrete makes it far more 
reliable, even from the compression standpoint. It prevents cracks 
in the concrete, and it also permits the use of a much higher unit- 
pressure than would be considered good practice in the use of plain 
concrete. This advantage becomes especially great in the con- 
struction of arches of long span, since in such a case the dead load 
is generally several times as great as the live load. Therefore the 
maximum variation in the line of pressure produced by any possible 
change in loading is not very great; and any method which will per- 
mit the use of a higher unit-pressure in the concrete is fully justified 
by the use of such an amount of steel as is required in this case. 

423. Elements of Integral Calculus. It has been found im- 
practicable to develop the theory of elastic arches without employing 
some of the fundamental principles of integral calculus; but an effort 
will be made to explain each one of the equations which are used, in 
such a way that the application of calculus to this particular case 
may be understood. To facilitate this demonstration, a few of the 
fundamental principles of integral calculus will be briefly demon- 
strated. All of the calculus equations which are used are similar to 
Equation 48. In this, a character J, somewhat similar to the letter 
S (which may be considered to stand for the word summation), is 
placed in front of some mathematical quantities. The equaton 
generally reads that this summation equals zero. The general 



398 MASONRY AND REINFORCED CONCRETE 

meaning of the equation is that there is a group of quantities all of 
which are in general similar, but which have a variation in magnitude. 
In general, some of these quantities are positive, and some are negative, 
and the equation reads that the summation or the algebraic addition 
of all these positive and negative quantities just equals zero; or, in 
other words, that the sum of all the positive quantities is just equal to 
the sum of all the negative quantities. 

For example, the first one of the equations marked 48 may be 
interpreted as follows: M represents the transverse moment of the 
arch rib at any point of the arch rib. 'M is a variable, being sometimes 
positive, sometimes negative, and sometimes zero; E is the modulus of 
elasticity, and we shall here assume that this is also constant; ds 
represents the distance between any two consecutive sections of the 
arch rib. Theoretically, ds is assumed to be infinitely small, which 
means that we consider an infinite number of sections of the arch rib. 
I represents the moment of inertia of the arch rib at any section. In 
some cases this may be considered a constant; and it is a constant, 
provided the arch rib is of a uniform cross-section throughout its 
length. If, as is frequently the case, the arch rib is of variable cross- 
section, then the value of I is variable for each section. It is assumed 
that the moment at each section is multiplied by the distance ds 
between the consecutive sections, and divided by the product of the 
modulus of elasticity and the moment of inertia at that section. All 
these quantities are positive, except M, which is sometimes positive, 
sometimes negative, and occasionally zero. Whenever any term has 
a constant value for each one of these small products, it may be placed 
outside of the summation sign, since the summation of a constant 
quantity times a variable is, of course, equal to that same constant 
quantity multiplied by the summation of the variables. As a corollary 
of this, we may also say that if the summation equals zero, we may even 
take the constant term out altogether; since, if a constant times a 
summation of positive and negative terms equals zero, then the sum- 
mation of those positive and negative terms must of itself equal zero. 
There will be an illustration in the following sections, of the dropping 
of constant terms, and therefore the simplification of the mathematics. 
If such a product were obtained for each one of a very large number 
of cross-sections of the rib, we should have a series of products, some 
of which would be positive, some negative, and probably two of which 



MASONRY AND REINFORCED CONCRETE 399 

would be zero. The algebraic sum of these terms would equal zero. 
The letters and B near the top and bottom of the summation sign 
represent that sections are made all the way from to B in Fig. 228. 
If the sections had been taken between two other points (as, for 
example, between and C), the letter C would take the place of the 
letter B in the equation. 

The three equations of Equation 48 are given without demon- 
stration. The student must accept the equations as being mathe- 
matically true, since their demonstration involves work in integral 
calculus which cannot be here given; but it should also be realized 
that the equations are only precisely true when the number of terms 
is infinitely large, and the distance ds is therefore infinitely small. 
When the sections are taken at a finite distance apart, as it is practi- 
cally necessary to do, then there may be theoretically a slight error; 
but when the number of sections of an arch rib is made from 12 to 20 
in the length of the span, the inac- 
curacy involved because the num- 
ber of terms is not infinite is so 
very small that it is of no practical 
importance. 

424. Classification of Arch 

RibS. Arch ribs may be classified Fig. 228. Diagram Illustrating Theory 

1 . of Elastic xVrches. 

in three ways: first, those which 

have fixed ends and no hinges; second, those which haA^e a hinge or 
joint at each end; and third those which are hinged at both ends and 
in the center. The first class is by far the most common, and is the 
simplest and cheapest to construct; but, as will be developed later, 
it necessitates a very considerable allowance for temperature stresses 
which, under very unfavorable conditions, are even greater than the 
maximum stresses due to loading. The temperature stresses of a 
two-hinged arch are less severe, while those for a three-hinged arch 
may be neglected; but the construction of hinges in arch ribs adds 
considerably to the cost. 

425. Mathematical Principles. In the following demonstration, 
the arch rib is considered as a single line OCB (Fig. 228), which is as- 
sumed to have the properties of an arch rib — namely, the moment of 
inertia , modulus of elasticity of the material, and the consequent resist- 
ing moment. The curved line PQR represents the special equilibrium 




400 MASONRY AND REINFORCED CONCRETE 



polygon corresponding to some one condition of loading. Although 
this line is drawn as a curved line, it is assumed to be a curve which is 
made up of a large number of correspondingly short lines, each of 
which corresponds to a section of an equilibrium polygon similar to 
those described under "Youssoir Arches." This equilibrium polygon 
is yet to be determined. 

In Church's ''Mechanics of Engineering/' Chapter XI, is given 
the mathematical proof of three general equations which apply to this 
problem. No demonstration will here be made of these three equa- 
tions, which are as follows; 

B B B 

CKJ±-fi. C Mxds - n • C M y ds - o • (48^ 

J EV ~ > J EI u ' J EI u > " "■ v ' 

O 0.0 

The practical meaning of the first of these equations may be described 
as follows (see Fig. 228) : ds represents one of an even number of very 
short sections into which the length OCB of the arch rib has been 
divided. M represents the transverse moment acting on the arch 
rib at that section under the particular condition of loading which 
is being considered. E is the modulus of elasticity of the material, 
and I is the moment of inertia of the section. At some of the sections 
the moment is positive, and at some it is negative. The product of 
M and ds, divided by the product of E and I, is therefore sometimes 
positive and sometimes negative. According to this equation, the 
summation of these various products for each short section (ds) of 
the rib equals zero; or, in other words, the summation of the positive 
products will exactly equal numerically the summation of the negative 
products. 

The other two parts of Equation 48 must be interpreted similarly, 

the only difference being that in each case the term-=y is multiplied 

by the corresponding value of y for one of the equations, and by x for 
the other. This group of three equations (48) has nothing to do with 
the form of the special equilibrium polygon PQR. 

It may also be proved by analytical mechanics, that if the curve 
PQR represents the special equilibrium polygon corresponding to 
some system of loading, and z represents the vertical distance between 



MASONRY AND REINFORCED CONCRETE 401 



the arch rib and the special equilibrium polygon at any section, then 
the moment M at that section a of the rib, equals Hz, in which H is a 
constant which may be determined from the force diagram. The 
curve PQR represents a typical special equilibrium polygon which 
crosses the arch rib at two points. These points of intersection indi- 
cate points of contraflexure, where the transverse moment changes 
its direction of rotation, and where it is therefore zero. When the 
special equilibrium polygon is above the rib curve, we call the mo- 
ment positive; and when it is below, we call it negative. When it is 
positive, it means that there is tension in the lower part of the rib, and 
compression in the upper part. The conditions are, of course, the re- 
verse of this when the curve is below the rib. We may therefore sub- 
stitute Hz for the value of M in the group of Equations 48; and since 
H and E are both constant for all points, from the principle enunciated 
in Article 423, we may not only place them outside of the sign of sum- 
mation, but may even drop them altogether, since the summation 
equals zero; and we may therefore transform Equations 48 to the 
following : 

B B B 

p^-0; J*-^=0; f*JL*L = . ...-(49) 

o 

Whenever we are investigating the mechanics of an arch rib 

which has a constant moment of inertia, we may simplify Equations 

49 by dropping out altogether the I of the denominators of those 

equations; but since arch ribs are usually made with deeper sections 

near the abutments, the I will be greater near the abutments. Calling 

the I at the center I c , then J equals nl c , in which n is a variable. If 

we substitute this value of I in the denominators of Equations 49, 

then, since I c is a constant quantity, it may be placed outside of the 

summation sign, and even dropped altogether, which practically 

means that we substitute n for I in Equations 49. We shall also 

substitute for z its value z" — z' (see Fig. 228), and shall rewrite 

Equations 49 as follows, by making the substitutions: 

B B B 

C^ d s = 0; C^~" )X ds = 0; f £=*U * - ; ■ • (50) 

o 



402 MASONRY AND REINFORCED CONCRETE 

It will later be shown how we can draw a line (marked vm in Fig. 228) 
which will satisfy the following equations: 

B B 

f^-0, and fi**-0 (51) 

O O 

Since the arch rib (represented by the curve OCB) is assumed to be 
symmetrical about its center C, and since vm is horizontal, any posi- 
tion of vm which will satisfy the first of Equations 51 will also satisfy 
the second. 

It is another principle of the science of summations, that if we 
have a series of terms whose summation equals zero, and also have 
another series of terms whose summation equals zero, but whose terms 
are made up of the difference of two terms, one of which corresponds 
in each case to the terms of the first summation, then we may say 
that the summation of the other corresponding terms is likewise zero. 
For example, the first one of Equations 50 consists of a series of terms 
which may be rewritten : 

z" z' 

-ds -ds. 

n n 

The first one of Equations 51 is the summation of a series of 

z f 
terms, each with the form — ds. In each of these summations the 

n 

different terms corresponding to the variable values of z f exactly 

correspond. We may therefore say that the summation of a series 

z" 
of corresponding terms, each one of the form — ds, will exactly 

equal zero; and we may therefore write Equation 52 as given 

below. We may also combine the second part of Equation 50 with 

the second part of Equation 51 in a similar manner, and obtain 

Equation 53 as given below It will be found more convenient to 

separate the third part of Equation 50 into two summations, one of 

z" 
which consists of a series of terms — yds, and the other of a series 

. . z' n 

of terms consisting of — y ds; and since the difference of these sum- 

mations equals zero, then the summations must equal each other, and 
we may therefore write Equation 54: 



MASONRY AND REINFORCED CONCRETE 403 

B 

C Z "-ds = ; (52) 

J n 

O 
B 

ta - : • (53) 



Cz" 

I — X (h 
J n 



O 

B B 



J 



~" y r/.v = f-yds; (54) 





An infinite number of equilibrium polygons may be drawn which 
will satisfy Equation 52 and 53. An equilibrium polygon may be 
drawn by trial, and the values of the summations for each side of 
Equation 54 may be determined. But since the position of the line 
vm is definitely determined by Equation 51, then the value of the right 
side of Equation 54 is fixed, and we only need to alter the pole dis- 
tance of the trial equilibrium polygon in the inverse ratio of the re- 
quired change in z", and then Equation 54 will be satisfied. Since 
changing all the values of z" in the same ratio does not alter the satis- 
faction of Equations 52 and 53, the changing of the pole distance does 
not vitiate the previous work. The value for the true pole distance 
is thus obtained, by which the true .curve PQR may be graphically 
drawn out. We may then determine the moment at any point, 
which is the product of Hz for any point of the curve, in which z is the 
vertical distance between the center line of the arch rib and the finally 
determined equilibrium polygon, and H is the pole distance corre- 
sponding to that polygon. 

It will be shown later that the thrust and the shear for any point 
of the curve equal the projection onto the tangent and normal respec- 
tively of the proper ray of the force diagram. It should be noted that 
the above equations apply only to symmetrical arch ribs which have 
their abutments at the same level. Under such conditions, Equation 
53 is always satisfied when Equation 52 is satisfied. In the very 
rare cases where arches have to be designed on a different basis, some 
of the simplifications given above cannot be utilized, and the work 
becomes far more complicated. The solution of these very rare 
cases will not be given here. 



404 MASONRY AND REINFORCED CONCRETE 

426. Moment of Inertia of any Section. Assume that Fig. 229 
represents a portion of the cross-section of an arch at any point, the 
particular portion having a total depth h equal to the thickness of the 
arch at that point, and a unit-width b, which is presumably less than 
the total length of the arch parallel to its axis. Assume that there 
is reinforcement in both the top and bottom of this section, and that 
the reinforcement is placed at a distance of y F of the thickness of the 
arch from the top and the bottom, or from the extrados and the in- 
trados. The moment of inertia of the plain concrete without any 
reinforcement would evidently equal T ^- bh 3 . A transverse stress on 
such a section will cause the bars on one side of the section (say the 
bottom) to be in tension, while those in the top will be in compression. 
As already developed in the treatment of columns (Part III, Article 310), 
the steel which is in compression will develop a compressive stress 
which is in proportion to the ratio of the moduli of elasticity of the 
steel and the concrete; and we may therefore consider that the area 
of steel in compression at the top (calling its area A) is the equivalent 
of an area of concrete equal to Ar, in which r is as usual E s -f- E c . 
The exact position of the neutral axis in a section which is reinforced 
both in compression and in tension, depends upon the percentage of 
steel which is used; but when the percentage is as large as it usually 
is, the neutral axis is not far from the center of the section ; and since it 
very much simplifies the computations to consider it at the center of 
the section, it will be so considered, and the moment of inertia of the 
steel and concrete combined may be expressed by the equation : 

/ = ^ bh 3 + 2Ar(Ah) 2 (55) 

If, in any numerical problem, it is considered preferable to place 
the steel so that the distance of its center of gravity from the surface 
of the concrete is greater or less than 0.1 h, a corresponding change 
must be made in the second term of the right-hand side of Equation 55. 

Example. Assume that p = .015, and that the thickness of the arch h 
equals 15 inches. For a unit-section 12 inches wide, the area of the con- 
crete would be bh, which equals 180 square inches. Then 180X.015= 
2.70 = 2A, since A is the area at either top or bottom. Therefore A= 1.35. 

Assume that r = 12; Ah = .4 X 15 = 6; then, 

/ = T \ X 12 X 15 3 + 2 X 1.35 X 12 X 6 2 
= 3,375 + 1,166 
= 4,541. 



MASONRY AND REINFORCED CONCRETE 



405 



It should be noted from Equation 55, that when, as is usual, the 
area of the steel in the extrados and intrados remains constant, while 
the thickness of the arch varies, the increase in the moment of inertia 
is not strictly according to the cube of the depth, but increases in 
accordance with two terms, one of which varies as the cube of the 
depth, and the other as the square of the depth. To illustrate the 
discrepancy, let us assume that the depth of the arch at the abutment 
is 10 per cent greater than the depth at the crown; or that, applying 
it to the above numerical case, the depth at the crown is 15 inches, 
and at the abutment the depth is 16.5 inches. Then, since b, J, and 
r remain the same in Equation 55, 

the value of the moment of inertia (< b 

for the abutment would be: 



I = T \ X 12 X 16.5 3 + 2 X 1.35 
X 12 X 6.6 2 = 5,903. 

Using the approximate rule that I 

varies as the cube of h, we find 

that: 

/ = 4,541 X (1.10) 3 <; 

= 6,044, 



which is about two per cent in 
excess of the value found from 
Equation 55. Computing the mo- 
ment of inertia similarly on the 
assumption that the depth at the 
abutment is increased 50 per cent, 

so that it equals 22.5 inches, w T e find that the approximate rule will give 
a moment of inertia which is nearly 8 per cent in excess of the actual. 
Therefore, when the increase in the depth of the rib from the crown 
to the abutment is comparatively small, we may adopt the approxi- 
mation that the moment of inertia increases as the cube of the depth. 
When the variation is greater, the inaccuracy will not permit the util- 
ization of the simplified forms which this approximation allows. 

427. Value of n. Still another simplification may be made, on 
the assumption that the moment of inertia varies as the cube of the 
depth, and also that we may increase the depth of the rib as desired. 
Assume that the depth of the rib is increased so that at any point n = 




Fig. 229. Arch Cross-Section 



406 



MASONRY AND REINFORCED CONCRETE 



ds-^-dx (see Fig. 230); ds is always greater than dx, and n is a ratio 
varying from one upward. Then, on the assumption that: 

I_ W 

we may compute a series of values for h in terms of the height at the 

center h c which will correspond to various angles a. For each angle, 

we find the ratio between h and h c that will correspoxid to the value 

ds 
which n has for that particular angle on the basis that n = ~ . If we 

dx 

substitute this value of -^ in Equations 52, 53, and 54 , we shall have 

dx 

the following Equations: 

j dy f z" dx= (56) 

/ \i i \ . B 

J>A In! \ f z" x dx = (57) ■ 

Zski*- l-U-J \ J o 

^- ,\! . B » B 

^-^ f 2* ydx = f 2 A 2/ Jx- .... (58) 

Fig. 230. Determination of Value of n. ^ O * O 

The values of /t which cause ?i to vary in this way, are as given in the 
tabular form : 



a 


ds 

dX 


3 — 
h = h c T n 


a 


ds 

n — — - 
dx 


1> = /'c tf~* 


0° 


1.000 


1 . 00/? c 


60° 


2.000 


1.26/ic 


15° 


1.035 


1.01 


65° 


2 . 36G 


1.33 


30° 


1.155 


1.05 


70° 


2.924 


1.43 


40° 


1 . 305 


1.09 


75° 


3.864 


1.57 


45° 


1.414 


1.12 


80° 


5 . 759 


1 . 79 


50° 


1 . 550 


1.16 


S5° 


11.474 


2 . 25 


55° 


1 . 743 


1.20 


90° 


Infinity 


Infinity 



Therefore, when all sections have the same moment of inertia, 
and n is uniformly 1, use Equations 52, 53, and 54, ignoring the n. 
When an increase in depth of section, as indicated above, will fulfil 
the ultimate requirements, there is an advantage of simplicity in 
making the sections accordingly, and using the Equations 56, 57, 
and 58. \\ } kmi it proves necessary to vary the sections according 



MASONRY AND REINFORCED CONCRETE 



407 



to some different law, n must be determined at frequent intervals, 
spaced by a uniform ds, and the summations of Equations 52, 53, 
and 54 determined. The remainder of this method follows out the 

assumption that n varies as — , or that dx = — . 

dx n 

428. Position of vm. We may locate vm by satisfying Equa- 

B 

tion 51, which may be written j z f dxz=0. But this integral is 

represented by the shaded area (Fig. 231), which is the equivalent 
of saying that the segment OCB = the rectangle OK X OB. IWCB 
were a parabola, OK would exactly equal § CD. Even with circular 
arcs, the ratio § is approximately correct if the angle is small. There- 
fore, for flat circular arcs, draw vm at § the height of the arc. If neces- 
sary, increase the height according to the figures given in the accom- 
panying tabular form : 



2a 


Ratio 


Excess E 


moR 




10° 


.607 


0.04 


per 


cent 




15° 


.667 


0.09 


a 


" 




20° 


.668 


0.15 


" 


a 




25° 


.668 


0.21 


u 


it 




30° 


.669 


. 35 


" 


it 




40° 


.671 


0.62 


" 


a 




. 60° 


.676 


1.42 


a 


a 




90° 


.689 


3.35 


a 


" 




180 


.785 


17.8 


a 


it 



Of course, for full-centered arches in which 2 a = 180°, the error of 
the | rule is very great, but the tabular values are correct. 

Since an elliptic arc may be considered as a circle in which the 
vertical ordinates have all been shortened by some constant ratio, the 
same law and same percentage of error will hold true. 

For any other curve, particularly multi-centered curves, the 
position of vm may be found by determining by trial a position such 
that the summation of equally spaced ordinates is zero. 

429. Weight and Thickness of Arch. Theoretically, this 
should be known before any calculations are made; but since the 
weight of filling and pavement are always large, and their unit-weight 



408 MASONRY AND REINFORCED CONCRETE 

is but little less than that cf the concrete, it is possible to estimate 
from experience on the required crown thickness, and to make the 
thickness at other points in the required ratio. If this should prove 
too thin (or too thick), all sections can be changed in the same ratio. 
If the outline of the intrados is determined (as in the case of an arch 
spanning railroad tracks), and the upper surface line (of earthwork 
or pavement) is also known, the change in the arch ring will mean 
only a change in weight due to the difference of unit- weight of con- 
crete and earth filling. If the original assumption is even reasonably 
close, this difference will hardly exceed the uncertainties in the 
loading. 

430. Intrados. The span and rise are frequently predetermined. 
Fortunately this method is applicable to almost any form of curve, if 
. the change in curvature is not too 

extreme. Even if the arch is very 
flat and the curvature very sharp 
near the abutments, it only means 
that the virtual abutment is some- 
where on the haunches. There- 
fore, draw the intrados; assume 

and lav off a reasonable crown 

t/ 

thickness; multiply this thickness 
by the factors given in the tabular form in Article 427 for the angles 
with vertical lines made by the various normals to the curve. These 
thicknesses can be laid off, and the extrados can be drawn through 
the points. 

But since the curve OCB of Fig. 228 does not represent either the 
intrados or extrados, but the center line of the rib, we should draw a 
line midway between the intrados and extrados which will represent 
the center line of the rib, and which corresponds to the line 
OCB in the figures which refer to the theoretical demonstrations. 
This also means that the span of the rib, measured between the centers 
of the skewbacks, will be slightly greater than the nominal clear span. 
The rise of the center of the rib above the line joining the abutment 
points and B will in general be slightly different from the nominal 
rise of the arch. 




Fig. 231. Determination of Position of vm. 



MASONRY AND REINFORCED CONCRETE 



409 



COMPLETE SOLUTION OF NUMERICAL PROBLEM 
ELASTIC ARCH 

431. Dimensions of Arch. We shall apply the above prin- 
ciples to the design of a segmental arch having a span of 60 feet and a 
rise of 15 feet. To find the radius for the intrados which will fulfil 
these conditions, we may note from Fig. 232 that the angle O'B'C is 
measured by one-half of the arc O r C, and therefore O'B'C is 
one-half of the angle a; but the angle 0'B r C f is an angle whose 
natural tangent equals 15 -s- 30, or precisely 0.5. The angle whose 



live load-zoo" 




Fig. 232. Reinforced-Concrete Arch Rib, Fixed Ends. 

tangent has this value is 26° 34', and therefore a equals 53° 8'. To 
find the radius, we must divide the half-span (30) by the sine of 53° 8', 
and we find that the radius equals 37.50 feet. 

For the depth of the keystone we can employ only empirical rules. 
The depth as computed from Equation 47 would call for a keystone 
depth of about 27 inches, which would be proper for an ordinary 
masonry arch; but considering recent successful practice in rein- 
forced-concrete arches, and the far greater reliability and higher 
permissible unit-stresses which may be adopted, we may select about 
§ of this — or, say, 18 inches — as the depth of the arch ring at the crown. 



410 MASONRY AND REINFORCED CONCRETE 



We shall compute the depth the arch ring should have at various 

points, according to the tabular form in Article 427, so that the mo- 

. ds 
ment of inertia will vary in the ratio — , which will make Equations 

56 to 58 applicable. An arc of 1 degree equals .0175 of the radius, 
and therefore an arc of 1 degree on a circle with a radius of 37.5 feet 
will have a length of .6545 foot. At a distance of 15 degrees from the 
center, or at a distance of 9.82 feet, the depth is one per cent greater 
than the depth at the center, or it is 18.18 inches deep. 

At 30 degrees from the center, or at a distance of 19.63 feet 
measured on the arc, the depth is 5 per cent greater, or it is 18.90 
inches deep. At a distance of 40 degrees from the center, or 26.18 
feet measured on the arc, the value of h is 9 per cent greater, or it is 
19.62 inches. At 45 degrees from the center, or 29.45 feet measured 
on the arc, h is 12 per cent greater than the center depth, or the depth 
is 20.16 inches. At 50 degrees from the center, or 32.72 feet measured 
on the arc, h is 16 per cent greater, or its thickness is 20.88 inches. At 
the abutment, which is 53° 8' from the center, the thickness should be 
(by interpolation) about 18 per cent greater than at the center, or it 
should be 21.24 inches, or say 21 J inches. 

Laying off these various distances from the center on the in- 
trados, and measuring radial distances at each point to represent the 
proper thickness at the several points, we may join the various points 
and obtain the curve of the extrados. Bisecting each one of these 
several arch thicknesses will give us a series of points which are points 
on the center line of the arch rib. We thus find that the actual span 
may be considered as 61.40 feet, and that the rise is scaled at 15.25 
feet. 

432. Position of vm. When the center line of the rib is a parab- 
ola, we may lay off vm by drawing it at a height J of the rise above 
the line OB. Even when it is a circle, it is comparatively easy to com- 
pute with mathematical accuracy the height of OK, by computing the 
area of the segment OCB, and dividing it by the length of the line OB. 
As previously explained in Article 428, the two-thirds rule may be 
used even for circular arcs, when the arch is very flat. In this partic- 
ular case, the two-thirds rule is far from applicable; and since for 
multi-centered curves no such rule is applicable, the general method 
will be here given. We divide the 1 span (61.40) into 20 equal parts. 



MASONRY AND REINFORCED CONCRETE 411 

Practically this is most easily done by setting a pair of dividers by 
trial so that 10 equal spaces may be stepped off in the length of the 
half-span. From these division points on the line OB, erect perpendic- 
ulars to the center line of the w arch rib OCB. The area of a curve 
bounded by a straight line at the bottom, and which has vertical and 
equally spaced ordinates, may be computed with very close accuracy 
by the adoption of Simpson's rule. If y represents the ordinate at 
the beginning of the curve (and in this case y = 0), while y t up to 
y n represent the lengths of the several ordinates (y n being the last ordi- 
nate, and, in this case, also equal to 0; and n being equal to the even 
number of divisions, in this case 20), then the area may be expressed 
by the formula : 

Area = 3H2/0 + 4 {y 1 + y 3 + . . .?/,„_,,)+ 2{y 2 + y 4 + y (n _ 2) )+ y n I 

(59) 

Applying this rule, we find that the area will be 640.50 square feet. 
Dividing this by the span, 61.40, we find that the height of vm above 
the line OB will be 10.59 feet. The approximate two-thirds rule 
would give us 10.17. Making a rough interpolation in the tabular 
form of Article 428, we could say that for an angle 2 a equal to 106° 16'» 
the quantity to be added to the result by the two-thirds rule would be 
approximately 5 per cent. Adding 5 per cent to 10.17, we would have 
10.68, which gives a rough check with the far more accurate value just 
found. 

433. Laying Off the Load Line. We shall assume that the arch 
carries a filling of earth or cinders weighing 100 pounds per cubic 
foot, that the top of this filling is level, and that it has a thickness of 
one foot above the crown. Since concrete weighs about 150 pounds 
per cubic foot, we shall assume this weight of 150 pounds as the unit 
of measurement, and therefore reduce the ordinates of earthwork to 
the load line for the top of the earth, as shown in Fig. 232. We shall 
assume as an additional dead load a pavement weighing 80 pounds 
per square foot, and shall therefore lay off an ordinate of y 8 /-^ of a^ foot 
above the ordinates for the earth-filling load. For this particular 
problem, we shall only investigate a live load of 200 pounds per square 
foot, extending over one-half of the span from the abutment to the 
center. From our previous work in arches, we know that such a 



412 



MASONRY AND REINFORCED CONCRETE 



loading will test the arch more severely than a similar unit live load 
extending over the entire arch; and therefore, if the arch proves 
safe for this eccentric load, we may certainly assume that it will be 
safe for a full load. These load lines are laid off similarly to the 
method elaborated in Article 409. The arch has already been laid off 
in equal horizontal sections, each having a width of 3.07 feet. The 
two end sections are slightly longer if we consider the entire load 
which is vertically over the extreme ends of the extrados of the arch. 
The 18 sections lying between the end sections, have a width of 3.07 
feet, and a variable height which may be considered as extending 
from the top of the load line down to the intrados. We may therefore 
multiply the widths of these sections by their various heights, and by 
150, and obtain the number of pounds weight on each section, and 
we find the loads as follows : 



No. of Section 


Loading 


No. op Section 


Loading 


1 


6,860 


11 


1,889 


2 


4,589 


12 


1,957 


3 


3,860 


13 


2,095 


4 


3,070 


14 


2,173 


5 


2,526 


15 


2,716 


6 


2,102 


16 


3,140 


7 


1,757 


17 


3,684 


8 


1,481 


18 


4,474 


9 


1,343 


19 


5,203 


10 

• 


1,275 


20 


7,620 



The sum total of this loading, which represents the total dead and 
live load on a section of the arch one foot wide (in the direction of the 
axis of the arch), is 63,814 pounds. We lay off these various loads on 
the right-hand side of the drawing in a vertical line, using a scale of 
5,000 pounds per inch. Selecting a pole o x at random, we draw rays 
to the various points in the load line. 

434. Trial Equilibrium Polygon. Commencing at the point 
0, we draw the segments of the trial equilibrium polygon parallel 
with the rays in the force diagram which run from the point O v to the 
load line, and obtain the trial equilibrium polygon OB v By drawing 
from o l the line o x n parallel to the line OB v we obtain the point n on 
the load line, from which we draw an indefinite horizontal line which 



MASONRY AND REINFORCED CONCRETE 413 

will be the locus of the pole of the true equilibrium polygon. A 
vertical from the point o t intersects the horizontal from n in the point 
o 2 , and this would be the pole of a trial equilibrium polygon whose 
closing line is horizontal, and whose vertical ordinates are equal to 
those of the corresponding vertical ordinates of the trial equilibrium 
polygon OB v It is only necessary to find the proper ratio by which 
these several ordinates should be multiplied, in order to find the corre- 
sponding ordinates of the special equilibrium polygon. It is also 
necessary to shift the entire trial equilibrium polygon up or down, 
so that the line v'"m'" which corresponds to it shall coincide with the 
line vm which has already been drawn. The special line v'"m'" 
corresponding to this trial equilibrium polygon, is found by satisfying 
Equation 56; but since dx is in this case a constant, it is found by 
determining the average value of z'", which is the distance from any 
point in the trial equilibrium polygon to the proper position of the 
line v'"m'" corresponding to this equilibrium polygon. If the trial 
equilibrium polygon had been again redrawn with 2 as a pole, it 
should terminate in the point B; but it is practically unnecessary to 
do this, since we may draw the line vm' parallel to 0B V and measure 
the distance from vm' down to the various points of the trial equilib- 
rium polygon 0B X . These various distances in the column headed 
z'" are as given in the accompanying tabular form (page 414). 

We have here the rather unusual case that the trial equilibrium 
polygon is entirely below the line vm' ; and the ordinates are all 
negative, instead of being partially positive and partially negative. 
In any case, the algebraic sum should be taken, which should be 
divided by the number of ordinates. In this case we find that the 
mean value of z'" is —3.44. Drawing the line v'"m'" parallel to vm! , 
and at a vertical distance of 3.44 feet below it, we find the position 
of the vm line for the trial equilibrium polygon 0B V This line in- 
tersects the trial equilibrium polygon at the points h" and k" . The 
student should note that it is a mere accidental coincidence that 
the point k" comes almost exactly on the intrados. By drawing ver- 
ticals from h" and k" to the line vm, we obtain the points h and k, 
which will be two points in the true equilibrium polygon. 

435. Pole Distance of the True Equilibrium Polygon. It is 
necessary to satisfy Equation 58. We shall consider in this case that 
the various points in the arch-rib curve and in the special equilibrium 



414 



MASONRY AND REINFORCED CONCRETE 





y 


z> 


yz' 


z" ' 


z" 


yz" 


1 


1.55 


-9.04 


- 14.01 


- 9.50 


-6.06 


' - 9.39 


2 


5.15 


-5.44 


- 28.00 


- 7.15 


-3.71 


- 19.11 


3 


7.65 


-2.94 


- 22.50 


- 5.50 


-2.00 


- 15.76 


4 


9.70 


-0.89 


- 8.64 


- 4.20 


-0.76 


- 7.38 


5 


11.35 


+ 0.76 


+ 8.64 


- 3.20 


+ 0.24 


+ 2.72 


6 


12.70 


+ 2.11 


+ 26.80 


- 2.35 


+ 1.09 


+ 13.84 


7 


13.75 


+ 3.16 


+ 43.45 


- 1.70 


+ 1.74 


+ 23.93 


8 


14.45 


+ 3.86 


+ 55.80 


- 1.25 


+ 2.19 


+ 31.65 


9 


14.95 


+ 4.36 


+ 64.45 


- 0.90 


+ 2.54 


+ 37.95 


10 


15.20 


+ 4.61 


+ 70.07 


- 0.65 


+ 2.79 


+ 42.40 




15.20 






- 0.55 


+ 2.89 




11 




+ 43.90 


12 


14.95 




- 73.15 


- 0.60 


+ 2.84 


+ 42.45 


13 


14.45 
13.75 




+ 269.21 


- 0.80 

- 1.20 


+ 2.64 
+ 2.24 


+ 38.15 


14 




+ 30.81 


15 


12.70 




+ 196.06 


- 1.80 


+ 1.44 


+ 18.27 


16 


11.35 






- 2.60 


+ 0.84 


+ 9.53 


17 


9.70 






- 3.65 


-0.21 


- 2.04 


18 


7.65 






- 5.05 


-1.61 


- 12.32 


19 


5.15 






- 6.85 


-3.41 


- 17.56 


20 


1.55 






- 9.35 


-5.91 


- 9.16 














+ 335 . 60 




212.90 




+ 392.12 


-68.85 
- 3.44 




- 82.72 




+ 252.88 



polygon are the points where these two lines are intersected by the 
load lines through the centers of the 20 sections. Therefore the 
points where these verticals intersect the center of the arch rib, give 
the points from which we measure down to the line OB, and obtain 
various values for y which are given in the tabular form above (Article 
434). From Fig. 228 we may observe that z' equals the numerical 
difference between the value of y and the distance from OB up to 
the line vm. This distance has already been computed at 10.95 feet. 
Therefore, having scaled off as accurately as practicable the various 
values of y, it is unnecessary to scale off the values of z', but merely 
to take the numerical difference (carefully observing the algebraic 
sign) between 10.59 and the various values of y. We thus obtain the 
values of z' as given in the tabular form. Since z' measures the ordi- 
nates to points in the curve, and since the curve is symmetrical about 
its center, it is unnecessary, in this case, to set down the values of z f on 



MASONRY AND REINFORCED CONCRETE 415 

both sides of the center ; and therefore only the values from 1 to 10, 
inclusive, are written down in the tabular form. Multiplying the 
corresponding values of y and z' ', we find the products as given under 
the heading yz r . Adding these products for the half-span of the arch, 
we find an algebraic summation of + 196.06; multiplying this by 
2, we find that the algebraic summation for the entire arch is + 
392.12. 

The ordinates z" are measured from vm to the trial equilibrium 
polygon when it has been shifted not only so that its closing line is 
horizontal, but also shifted vertically (up or down) so that its line v'"m" f 
corresponds with vm; but it is unnecessary to draw it in that way, since 
we may measure the ordinates from the transposed line v m', because 
we know that they are in each case the equal of the ordinates as they 
would be if the transposition had been actually made. But the lengths 
of these ordinates below vm! have already been determined; and 
since we know that v f " m"' is 3.44 feet vertically below vm! , we need 
only change the ordinates z" f by 3.44 (taking care of the algebraic 
sign), and we then obtain the values of z" as given in the tabular form. 
Multiplying each value of z" by the corresponding value of y, we 
obtain the various values (plus and minus) for yz" as given in the last 
column of the tabular form. The algebraic sum of these quanti- 
ties is + 252.88. 

Since this value is less than the value of the summation of yz f , 
we must select a smaller value of H, so that the values of z" will be 
proportionately larger. We must therefore use a pole distance which 
shall be smaller than 2 n in the ratio of 252.88 to 392.12. To solve 
this graphically, we must draw an indefinite line ns, and lay off the 
distance ns equal to 392.12, at any convenient scale. Laying off a 
distance nt at the same scale so that it equals' 252.88; we may then 
join s and0 2 , and draw a line from t parallel to sO v obtaining the point 
3 which is the required pole of the special equilibrium polygon. 

436. Locating the True Equilibrium Polygon. We know that 
the segments of the true equilibrium polygon must be parallel with 
the rays of the force diagram which has its pole at 3 , and also that 
it must pass through the points h and k on the line vm. The point h 
lies between loads 4 and 5; therefore we draw through the point h 
a line parallel to the ray of the force diagram from 3 to the point on 
the load line between load 4 and load 5. Similarly, since the point k 



416 MASONRY AND REINFORCED CONCRETE 

lies between loads 16 and 17, we may draw through k a segment of 
the equilibrium polygon which is parallel to the ray from 3 to the 
point on the load line which is between load 16 and load 17. In 
order to avoid inaccuracy, the segments of the equilibrium polygon 
should be drawn from these two segments each way toward the crown 
of the arch and each way toward the abutments. As a check on the 
work, these separate sections of the equilibrium polygons should 
accurately meet at the top of the arch, and they should also reach the 
last verticals through and B at points which are on the same hori- 
zontal line. It is merely a coincidence that these points 0" and B" 
are almost exactly at the same level as the lowest point of the skew- 
backs. 

437. Maximum Moment under this Loading. An inspection 
of the diagram shows what might be expected, that the maximum 
moment occurs on the right-hand side of the arch, nearly under the 
center of the live load and very near to load 16. At this point the 
vertical distance z, between the equilibrium polygon and the center of 
the arch rib, is 0.55 foot, or 6.6 inches. The pole distance 3 n, scaled 
at 5,000 pounds per inch, indicates 22,650 pounds; therefore the 
moment at that point equals 22,650 X 6.6 = 149,490 inch-pounds. 
It may be observed, also, that the moment at the abutment scales 
exactly the same quantity, as nearly as it can be measured, but the 
moment is of contrary sign. In other words, the intrados will be in 
tension under load 16, and in compression at the two abutments. If 
this arch were reinforced with f-inch bars spaced 12 inches apart, in 
both the top and the bottom, there would then be two such bars in 
each section of the arch one foot wide ; and the area A (see Equation 
55) would be the area of one such bar, or 0.56 square inch. Since 
the depth of the arch at the abutment (h) is 21.25 inches, then Ah 
equals 8.5; and, by substituting these quantities in Equation 55, 
we find that the moment of inertia is : 

I = J s X 12 X 21.25 3 + 2 X 0.56 X 12 X 8.5 2 
= 9,593+ 971 
= 10,564 bi-quadratic inches. 

Then, transposing the equation M = — into the equation p = , 

e i 

we may substitute for M the value 149,490; for e the half-depth of 

the beam, 10.625; and for J the value found above, 10,564; and find 



MASONRY AND REINFORCED CONCRETE 417 

that the unit-stress in the concrete at the abutment equals about 151 
pounds per square inch. 

For this particular case of loading, the moment at the crown is 
almost zero, since it may be observed from the drawing, that the 
special equilibrium polygon crosses the center line of the rib about 
18 inches at the right of the center. This crossing indicates a point of 
contraflexure where there is no moment. Also, since the equilibrium 
polygon is below the center line of the rib at the crown, it indicates 
that such moment as there is for this loading is negative ; or, in other 
words, the tension is on the upper side of the rib. This same kind 
of moment exists on the entire left-hand side of the arch for this 
loading. It should also be observed that there is another point of 
contraflexure a few feet from the right-hand abutment. It will be 
shown later that the thrust at the abutment has a greater intensity per 
square inch than the maximum compression or tension due to moment. 
This practically means that the compression side of the arch is sub- 
jected to the combined compressions due to thrust and moment; while, 
on the other side, the thrusf more than neutralizes the tension, and 
actually relieves it altogether. 

Near the crown of the arch, the thrust is not so great, and will 
not wholly neutralize the tension due to moment. In order to with- 
stand the various stresses, the rib must have a larger cross-section 
than would be required for moment alone. This means that the 
equation developed in Article 271, Part III, Af = 62 bd 2 , can be utilized 
only in a roundabout way. For example, the moment at the abut- 
ment was computed above as 149,490 inch-pounds. But a section 12 
inches wide and 19.125 inches deep to the reinforcement, should with- 
stand a moment of 272,300 inch-pounds with 0.43 per cent of steel. 
The above moment is only 55 per cent of this. Therefore 55 per cent 
of the steel, or .55 X .00436<i = .002366c? of steel, could safely carry 
the tension. But the actual ratio of steel adopted was .00245. As 
shown above, the steel at the abutment is unnecessary for transverse 
moment and for this condition of loading. Nearer the crown, the 
moment is less; but the relief to tension afforded by thrust is very 
much less, and the steel has much more to do. With other conditions 
of loading, it will also be different; and therefore the same amount 
of steel f-inch bars spaced 12 inches, in both top and bottom, is used 
throughout. 



418 MASONRY AND REINFORCED CONCRETE 



438. Maximum Thrust Due to this Loading. The thrust at any 
point of the arch is measured by the projection onto the tangent to 
the arch at that point, of the corresponding ray of the force diagram. 
Since the rays of the force diagram which are parallel to the segments 
of the equilibrium polygon are approximately tangent to the arch rib, 
it is approximately true to measure the thrust at any point by measuring 
the corresponding rays of the force diagram; but a more precise 
value may be found by drawing a line from one end of a ray parallel 
to the corresponding tangent, and projecting the ray on it. This 
method is particularly useful, since it measures at the same time the 
amount of the shear at that point, as will be explained in the next 
article. Since the increase in the thickness of the arch is compara- 
tively slight from the crown to the abutment, in this particular problem, 
and since the amount of the thrust evidently increases very rapidly 
toward the abutment, the critical point, so far as the thrust is con- 
cerned, is evidently at the abutment. Therefore we may draw from 
the lower end of load 20, a line parallel to the tangent to the curve at 
the abutment, and obtain the line wx, which scales 40,200 pounds, 
and which therefore measures the thrust at the abutment. Since 
the abutment is 21.25 inches thick, the area of a section one foot 
wide is 255 square inches. Dividing this, in to 40,200, we have a 
quotient of 158 as the unit-compression per square inch due to thrust. 
Adding the value of the compression at the intrados which is due to 
moment (151), to the compression just found for thrust, we have a total 
of 309 pounds per square inch at the abutment. This compression 
does not allow for temperature stresses, which will be computed later, 
and which may exist simultaneously with the stresses due to moment 
and to thrust. 

439. Shear at Any Section. The shear at any section is meas- 
ured by the projection onto the normal to the arch rib, of the corre- 
sponding ray of the force diagram. It is seldom that the shear is a 
serious factor in the design of an arch. Whenever (as in the case 
just being worked out) the equilibrium polygon coincides approxi- 
mately with the arch rib, the shear is very small. When the amount 
of the thrust is definitely computed, as determined above, the amount 
of the shear at the same point may be readily determined at the same 
time. 



MASONRY AND REINFORCED CONCRETE 419 

For example, the shear at the abutment is the projection of the 
ray 3 x onto the line 3 w, which is parallel to the normal to the curve 
at B. This line, scaled at the rate of 5,000 pounds per inch, indi- 
cates a shear of about 2,200 pounds. Dividing this by 225, the area 
of the section of the arch at that point, the unit-shear is less than 10 
pounds per square inch, which of course may be neglected. The 
shear in any arch may be very easily tested by noting the portion of 
the special equilibrium polygon which makes the largest angle with 
the direction of the arch rib at any point; the larger the angle, the 
greater the shear. If the arch is tested at that point, and the shear is 
found to be insignificant, or well within the power even of plain con- 
crete to carry, there is no need for further investigation. 

On the other hand, there are minor stresses which occur in arches 
as well as other concrete structures, which must be provided for. 
These are caused by a possible excessive concentration of loading; 
possible structural weakness due to a poor quality of concrete in com- 
paratively limited areas ; the effect of slight settlement of the founda- 
tions, etc. On account of these various stresses, which are more or 
less non-computable, it is the usual practice to insert bars, which are 
not only useful in taking up shear, but also tend to bind the whole 
structure together, make it act more nearly as a unit, and permit the 
structural weakness in local spots to be made up by the strength of 
the sounder portions of concrete around it; and therefore shear bars 
are put in, such as are illustrated in Fig. 235. These bars are laced 
between the upper and lower sets of bars that run parallel with the 
axis of the arch. By this means, not only are the upper and lower 
sets of reinforcing bars tied together, but the bars have such a di- 
rection that they can take up any shearing force which may, by any 
chance, be developed. 

440. Temperature Stresses. The provision which should be 
made for temperature stresses in a concrete arch, is often a very 
serious matter, for the double reason that the stresses are sometimes 
very great, and also because the whole subject is frequently neglected. 
It will be shown later that the stresses due to certain assumed changes 
of temperature may be greater than those due to loading. There is 
much uncertainty regarding the actual temperature which will be 
assumed by a large mass of concrete. The practice which is common 
and proper with metal structures, is not applicable to masonry arches. 



420 MASONRY AND REINFORCED CONCRETE 

A steel bridge, with its high thermal conductivity, will readily absorb 
or discharge heat; and it is usually assumed that it will readily acquire 
the temperature of the surrounding air. On the other hand, con- 
crete is relatively a non-conductor. No matter what changes of 
temperature may take place in the outer air, the interior of the con- 
crete will change its temperature very slowly. One test bearing on 
this subject was conducted by burying some electrically recording 
thermometers in the interior of a large mass of concrete, and recording 
the temperatures as they varied for a period of ten months, which 
included a winter season. It was found that the total variation of 
temperature was but a few degrees. 

It is probably safe to assume that even during the coldest of 
winter weather the temperature of the interior of a large mass of 
concrete will not fall below that of the mean temperature for the 
month. Since the Weather Bureau records for temperate climates 
show that the mean temperature for a month, even during the winter 
months, is but little if any below freezing, it may usually be assumed 
that for concrete a fall of 30 degrees below the temperature of con- 
struction (say 60°) will be a sufficient allowance. A rise of tempera- 
ture to 90° F. is probably much greater than would ever be found in 
an arch of concrete. The earth and pavement covering protect the 
arch from the direct action of the sun. Even in the hottest day, the 
space under a masonry arch seems cool, and the real temperature of 
the masonry probably does not exceed 70°, even if the outer air 
registers 95°. If we therefore calculate the stress produced by a 
change of temperature of 30 degrees from the temperature of con- 
struction, we are probably exceeding the real stresses produced. 
Even if this extreme limit should be sometimes exceeded, it simply 
lowers temporarily the factor of safety by a slight percentage. The 
following demonstration, which has been adapted from that in Church's 
"Mechanics" (Section 385), will be described, but without demon- 
strating the fundamental equations, which depend on elaborate 
mathematical reasoning. Assume that: 

L = The length of the arch, measured in inches; 
t = Temperature, in degrees, Fahrenheit; therefore t — t represents the 

change of temperature expressed in degrees, Fahrenheit; 
c — Coefficient of expansion for concrete, which is here assumed to be 00000G.5; 



MASONRY AND REINFORCED CONCRETE 



421 



H t = Imaginary horizontal forces which would produce the same stress on 

the arch as that produced by any assumed change of temperature; 
d = Height of the line of action of H t above the abutment level. 

The other symbols are as previously used. In Fig. 233, the heavy 
full line between and B represents the arch rib in its normal and un- 
strained condition. If it were free to expand, it would assume some 
such form as indicated by the dotted line O'C'B' '; but since the arch 
is fixed at the abutments, the arch rib is forced to preserve the same 
distance between the abutments, and the tangents to the rib at the 
abutments remain fixed in direction. The rib therefore is forced to 
the form C" B. Of course the relative distortion is enormously 
exaggerated. These two requirements furnish the data for the 
equations given be- 
low. If the arch rib 
were assumed to be 
extended by the ad- 
dition of the imagin- 
ary arms as shown, 
and the two equal I 
and opposite forces l" s 
(H { ) were acting as 
indicated, these 
forces would hold 
the arch rib rigid against the tendency to expand or to change its 
direction at the abutments. Considered as an example of the general 
case of an arch rib acted on by forces, we may consider that the arch 
rib is acted on only by these two equal and opposite forces H t . Their 
line of action is the vm of the problem, as previously explained; and 
d is therefore the distance from the abutment up to this line vm. The 
equation which is based on the fact that the span of the arch is not 
changed by the temperature, or that it does not expand from OB to 
O'B' , is as follows: 




Fig. 233. Temperature Stresses in Arch Rib. 



L(t-Qc 



Hi 
E 



'/: 



(y- d) y ds 
I 



(60) 



The fact that there was no change in direction of the tangents, gives 
rise to the equation : 

*f\-s>*-o (61) 



422 MASONRY AND REINFORCED CONCRETE 



As before, we must allow for the variable moment of inertia, /; but 

ds dec 
since I = nl c , and ds = ndx, then _ = — } and Equation 61 becomes : 



it f „"-""• 



s 



But since H t , E, and I c are all constants, we may drop them in this 
case, and write the equation : 

B 

(y-d)dx = 0. 
O 

Since d is a constant, this equation virtually means that the 
summation of all the y's between B andO equals d times the number of 
sections. But the summation of the y's, as shown in the tabular form 
in Article 434, is 212.90 feet, or 2,544.8 inches. Dividing this by 20, 
we have 127.24 inches, which is the value of d, or the height of vm 
above the abutment, and is the distance above the abutment of the 
line of action of the pair of imaginary forces H t which will produce 
the same stress in the arch as the assumed change in temperature. 
Equation 60 may be transposed so as to solve for H„ and we may 

write (substituting — for -y-)'. 

■*-c ■*■ 

L(t-t )c EI C 
H t = B — ' 

{y*-yd)dx 
O 



/ 



For practical use, we transform the denominator of the above ex- 
pression into the summation of y 2 — yd for each point, times the con- 
stant distance between these points (= 3.07 feet, or 36.84 inches). 
The various values of y are obtained by taking the figures in the 
first column of the tabular form in Article 434, and multiplying each 
by 12 to reduce to inches. Squaring the several values of 12y for 
half of the span, and adding the squares, we may multiply the sum 
by 2, and obtain 381,328 as the sum of the squares; but the sum of all 
the y's, times 12, equals 2,544.8, and we may multiply this by 122.74, 
and obtain 313,576 as the summation of yd. Subtracting this from 
the summation of y 2 , we have left 67,752, which, multiplied by the 
value of dx in inches (36.84), gives 2,495,984, which is the denominator 
of the above fraction. Computing I c , the moment of inertia of the 



MASONRY AND REINFORCED CONCRETE 423 

arch rib at the center, in a similar manner to the computation in 
Article 437, we find a value of 6,529 biquadratic inches. 

Substituting all the known values in the above equation, we have : 

„ 720X30 X. 0000065X2,400,000X6,529 

Ht=z 2,495,984 — -881. 

(y - d) for center - 183 - 127.2 = 55.8 

{y - d) for abutments = - 127.2 = - 127.2. 

The moment produced by the assumed change of temperature of 
30 degrees, is therefore as follows: 

At the center, 881 X 55.8 = 49,160 inch-pounds. 

At the abutments, 881 X (- 127.2) = - 112,063 inch-pounds. 

It was computed above, that a moment of 149,490 inch-pounds at 

the abutment would produce a unit-stress in the concrete of 151 

pounds per square inch; therefore a unit-stress produced in the 

112 063 
abutment by a moment of 112,063 pounds would be ■ A ' — - X 151 
J r 149,490 

= 113 pounds per square inch. In cold weather the effect of the 
moment due to temperature would be to produce compression at the 
intrados at the abutment, and tension at the intrados at the crown; 
but it was found above, that the compression at the intrados at the 
abutment due to transverse moment and to thrust totaled 309 pounds 
per square inch. Adding the stress due to temperature, we have a 
total of 422 pounds per square inch. If the reduction of temperature 
below the temperature of construction was more than 30 degrees, the 
stresses would be increased in direct proportion. If the reduction 
of temperature was, say, 40 degrees, instead of 30 degrees, the added 
stress due to temperature would be about 151 pounds per square inch. 
On the other hand, during warm weather, the effect of a rise in tem- 
perature will be to relieve the strain; and the net compression or 
tension will be less than that which would be due to direct loading and 
to thrust. For the loading which has been computed, the moment 
due to loading at the crown is very small, and is in the opposite direc- 
tion to the moment usually produced by a load over the entire arch. 
It is generally true, that in cold weather the arch is stressed by the 
sum of the stresses due to transverse moment, thrust, and temperature; 
in warm weather the stresses usually tend to counteract each other. 
Cold weather is therefore a critical time for an arch, and the time 
when an excess of live load would be particularly dangerous. 



424 MASONRY AND REINFORCED CONCRETE 

441. Stresses Due to Rib Shortening. The compression in a 
rib results in shortening the arch rib very slightly; and this produces 
precisely the same effect in altering the moment as an equivalent fall 
in temperature. For example, in the above case, we have at the abut- 
ment a thrust of 296 pounds per square inch; dividing this by E, the 
modulus of elasticity, 2,400,000, we have .0001233, the proportional 
shortening; dividing this by .0000065, the coefficient of expansion, 
we find that the thrust due to this rib shortening is the equivalent of a 
reduction of temperature of 19 degrees. Since we have found that a 
reduction of temperature of 30 degrees produced a unit-stress of 113 
pounds per square inch, a virtual reduction of 19 degrees would pro- 
duce a unit-stress of 72 pounds per square inch. Since such a stress 
is always the same as that due to a reduction of temperature, and since 
this always has the effect of increasing the stresses for usual loading, 
such unit-stress must be added to the value found above; therefore, 
adding this 72 pounds per square inch to the total previously found 
(422), we have a unit-compression at the intrados at the abutment, of 
494 pounds per square inch. 

442. Testing this Arch for Other Loading. A live load of 200 
pounds per square foot over the entire arch would unquestionably 
increase the thrust over the entire arch, especially at the abutments. 
The stress due to shortening will of course be increased in proportion 
to the increase in the thrust. The stress due to moment cannot be 
accurately predicted. Of course such an examination and test for 
full loading should be made in the case of any arch to be constructed, 
and should be worked out precisely on the same principles and in 
general by identically the same method as was used above. 

To test the arch for a concentrated loading such as would be 
produced by the passage of a road roller, or, in the case of a railroad 
bridge, by an especially heavy locomotive, the test must be made by 
assuming the position of that concentrated load which will test the 
arch most severely. Ordinarily this will be found when the concen- 
trated load is at or near one of the quarter points of the arch. The 
only modification of this test over that given above in detail, is in the 
drawing of the load line, but the general method is identical. 

443. Testing an Arch with Variable Moments of Inertia. It has 
already been indicated how the equations on which the arch theory 
is based may be simplified when the moment of inertia is constant. 



MASONRY AND REINFORCED CONCRETE 425 

The above problem was worked out on the basis that the moment of 

ds 
inertia varied in the ratio of - -. In either case the solution is con- 
da; 

siderably simplified. Arches are frequently designed where the mo- 
ment of inertia varies according to some other law. The very fre- 
quent practice is to increase the thickness of the arch toward the abut- 

ds 
ment much more rapidly than the -— rule would call for, and thus 

increase the moment of inertia of the arch much more rapidly. In 
such a case, Equations 49 must be used; and the summations must 
be made up by computing for each unit-section the value of the 
moment of inertia for that point, and by measuring ds along the length 
of the arch rib. This means also that the sections of dead and live 
load, instead of having a constant width (as in the above problem), 
have a variable width, and the loads must be separately computed. 
While there is nothing especially difficult about such a solution, it 
involves considerably more work. 

HINGED ARCH RIBS 

444. General Principles. The construction of hinged arches of 
reinforced concrete is very rare, but is not unknown, and will probably 
come into greater use when their advantages are more fully realized. 
We may consider that structurally they consist of curved ribs which 
have hinges at each abutment, and which may or may not have a hinge 
at the center of the arch. The advantage of the three-hinged arch 
lies in the fact that it is not subject to temperature stresses. The 
two-hinged arch is partially subject to temperature stresses, but not 
to so great an extent as the fixed arch, since the arch rib is not 
held rigid at the abutments as in the case of the fixed arch. Prac- 
tically the hinges are made by having at each hinge a pair of large cast- 
iron plates which are a little larger than the size of the rib, and which 
have at their centers a bearing for a pin of due proportionate size. 
The bearings are so made that one may turn, with respect to the other, 
about the axis of the pin through an angle of a very few degrees. 

445. Arch of Two Hinges. The third of Equations 4& must 
be satisfied, which practically means that Equation 54 must be satis- 
fied. This means that we must find a trial equilibrium polygon, and 
increase or decrease its pole distance so that the summation of thfc 



42G 



MASONRY AND REINFORCED CONCRETE 




products based 
on z" shall equal 
the summation 
of similar prod- 
ucts based on z' . 
But in this case 
the special equi- 
librium polygon 
passes through 
the abutment 
points, and there 
is no moment at 
the abutment. 
Therefore, after 
having found the 
pole distance of 
the special equi- 
librium polygon, 
we may draw the 
special equilib- 
rium polygon by 
commencing at 
one abutment 
point; and, as a 
check on the 
work, we should 
find that it passes 
through the other 
abutment point. 
The maximum 
moment due to 
temperature will 
be at the center 
of the arch rib, 
and will be based 
on an equation 
similar to Equa- 
tion 60, which 
may be used by 
calling d = o. 



MASONRY AND REINFORCED CONCRETE 



427 



Equation 61 does not apply, since the ends of the arch rib are 
free to turn at each abutment. 

446. Arch of Three Hinges. A three-hinged arch is a still more 
simple case, since none of the three fundamental equations (Equation 
48) which are used for fixed arches needs to be satisfied. It is only 
necessary to find the special equilibrium polygon which will pass 
through the two abutment hinges and the center hinge. There are 
no temperature stresses and no stresses due to the shortening of the 
rib. It may thus be said that a three-hinged arch is much more 
simple to calculate, and its stresses are more definite. The construc- 
tion of the hinges will of course add somewhat to the cost, and probably 




1 3-0 H 

Granolithic iidzwalh, 

*>>■:,» '.„.V;.?^- V itrified Stick Putter 
dirj y -l" ' I"". ^""""l^l" ■■•' • 



<T:n: ^^:;t v t^;- t*v^ ;r; 



^■""Sarj «.£'*8arj \^ : Barj iz"cc. 

Crojj Section T/iroufh Crown 
°Barj 3" from outside surface 



u£ 



filling 




Fig. 235. Reinf orced-Concrete Oblique Arch 



Graver's Lane Bridge, Philadelphia, Pa-r 



add more than any saving which might be made by a reduction in the 
cross-section of the arch. Probably the greatest advantage of three- 
hinged arches lies in their immunity from damage which may result 
from a settlement of the foundations. It has been assumed, in con- 
sidering the theory of fixed arches, that the foundations are abso- 
lutely immovable. A settlement of either abutment of a fixed arch 
with reference to the other abutment, will inevitably result in stresses 
in the arch rib which might easily be greater than any stresses to 
which the arch rib would be subjected either on account of the loading 
or through change in temperature. The failure of many arches is 



428 



MASONRY AND REINFORCED CONCRETE 



unquestionably due to this cause. An arch rib with either two or 
three hinges is absolutely immune from any such danger; and there 
is therefore a strong argument for the use of hinged arches when the 
arch must be placed on foundations which are so uncertain that a 
settlement of either foundation is quite possible. Of course an equal 
settlement of both, foundations would do no damage, but the equality 
of such a settlement could never be counted on. 

447. Description of Two Reinforced=Concrete Arches. In 
Figs. 234 and 235 are shown the details and sections of two reinforced- 
concrete arches having fixed abutments, which have been recently 
erected. The first bridge has a nominal span of 60 feet between the 
two faces of the abutments. On account of the great thickening of 
the arch rib near the abutment, the virtual abutments are practically 




Fig. 236. Stone Arch on Line of New York, New Haven & Hartford Railroad. 

at points which are approximately 26 feet on each side of the center. 
The method of reinforcing the spandrel and parapet walls is clearly 
shown in the figure. The side view also gives an indication of some 
buttresses which were used on the inside of the retaining walls above 
the abutments in order to reinforce them against a tendency to burst 
outward. 

Fig. 235 shows a bridge which is slightly oblique, and which 
spans a double-track railroad. The perpendicular span between the 
abutments is 34 feet, but the span measured on the oblique face walls 
is 35 feet 8 inches. In this case, similarly, the arch is very rapidly 
thickened near the abutment, so that the virtual abutment on each side 
is at some little distance out from the vertical face of the abutment 
wall. In both of these cases, the arch rib was made of a better quality 
of concrete than the abutments. 



MASONRY AND REINFORCED CONCRETE 429 

The arch of Fig. 234 was designed for the loading of a country 
highway bridge; that of Fig. 235 .was designed for the traffic of a city 
street, including that of heavy electric cars. 

448. Stone Arch. In Fig. 236 is shown a stone arch on the New 
York, New Haven & Hartford Railroad at Felhamville, N. Y. This 
arch was constructed over a highway, and the length of its axis is 
sufficient for four overhead tracks. The span is 40 feet, and the rise 
is 10 feet above the springing line, the latter being 7 feet 6 inches above 
the roadway. The length of the barrel of the arch is 76 feet. 

The arch is a five-centered arch, the intrados corresponding 
closely to an ellipse, the greatest variation from a true ellipse being 
1 inch. The theoretical line of pressure is well within the middle 
third, with the full dead load and partial live load, until the short 
radius is reached, where it passes to the outer edge of the ring-stone, 
and thence down through the abutment. There is a joint at the points 
where the radii change, to simplify the construction. 

The stone is a gneiss found near Yonkers, N. Y., except the key- 
stone, which is Connecticut granite, and the coping, which is blue- 
stone from Palatine Bridge, N. Y. 



INDEX 



Page 
A 

Absorptive power of brick 11 

Abutments 150, 360 

Arch culverts 163, 248 

Arch masonry 300 

Arch sheeting 300 

Arches 

kinds of 302 

theory of 351 

Arris, definition of S3 

Ashlar, definition of 83 

Asphalt waterproofing 04 

Asphaltum 07 

Atmospheric influences on stone . . 2 

Ax or pean hammer 83 

B 

Backing, definition of 360 

Basket-handled arch 362 

Batter 83 

Beam footings 115 

Bearing block 83 

Bed joint : 83 

Belt-course 84 

Bending bars 318 

beams and girders 321 

column bands 322 

Hunt bender 320 

slab bars 321 

spacers 322 

stirrups 322 

tables for 319 

unit frames 323 

Bitumen 67 

Blaw collapsible steel forms 309 

Bonding 84 

Bonding old and new concrete 58, 323 

Box culverts 247 

Brick 9 

absorptive power 11 

characteristics 9 



432 INDEX 



Page 
Brick 

classification of 12 

color of -. 11 

crushing strength 13 

definition 9 

fire 13 

requisites for good 11 

sand-lime . 14 

size and weight 12 

Brick masonry 96 

bonding used in , 06 

constructive features 97 

cost of 99 

efflorescence 99 

impermeability 99 

measuring, methods of 98 

strength of 98 

Brick piers 100 

Brick tests 13 

Bridge piers 153 

abutment 156 

failure, possible methods of 155 

placing of 153 

sizes and shapes of ' 154 

Broken stone 39 

classification of 39 

cost of ' 51 

size of 40 

uniformity of 40 

Building stone 6 

conglomerates 8 

dolomite 7 

granite 8 

limestone 6 

marble 6 

sandstone 7 

trap rock 8 

Bush-hammered 84 

Buttress 84 



Caissons 

open 

pneumatic 143 

Cast-iron piles 119 

Catenarian arch 362 

Cavil 84 

Cement, cost of 51 

Cement brick machines 295 



140 



INDEX 433 



Page 

Cement testing 21 

briquette 30 

chemical analysis 22 

constancy of volume 32 

fineness 24 

general conditions 33 

mixing 30 

moulding . . 31 

moulds 30 

normal consistency 25 

sampling 22 

specific gravity 23 

standard sand 29 

storage of test pieces 31 

tensile strength 32 

time of setting 27 

Cementing material 17 

lime 17 

natural cement 19 

Portland cement 20 

pozzuolana 19 

Centers for arches 311 

classes of 311 

forms for bridge at Canal Dover, Ohio 317 

form for, at 175th St., New York 315 

Charging mixers 284 

Chisel 84 

Cinder concrete * 51 

Cinder vs. stone concrete 68 

Cinders for concrete 42 

Circular arch . . . 362 

Clay puddle 104 

Cofferdams 138 

Columns 248 

design of 250 

eccentric loadings of, effect of 255 

hooped 253 

reinforcement, methods of 248 

Compressive soil, improving 109 

Compressive strength of concrete 49 

Concrete 47 

cinder 51 

compressive strength of 49 

cost of 51 

depositing 57 

fire and water tests of 72 

fireproofing qualities of 70 

freezing of, effects of 59 



434 



INDEX 



Concrete 

mixing, cost of 

mixing, methods of 54 

modulus of elasticity 

proportioning 

ramming 

rubble 

shearing strength 

steel for reinforcing 

tensile strength '.' 

transporting 

waterproofing 

water-tightness of 

weight of 

wetness of 

Concrete block machines 

Concrete building blocks 

cost of making 

curing of 

material for making 

mixing and tamping 

mixture for facing . • 

proportions 

size of 

Concrete curb 

construction 

cost 

types of. .* ' 

Concrete masonry 

foundations 

rubble 

Concrete piles 

Raymond : 

Simplex 

Concrete walks 

concrete base 

drainage of foundations 

seasoning * 

top surface 

Concrete work, machinery for 

boilers 

hoisters 

gasoline engines i 

measuring devices 

mixers 

motors 

plant 

plant for Locust Realty Co 



Page 

51 

74 

50 

47 

58 

51 

50 

70 

50 

57 

63 

81 

51 

56 

294 

14 

17 

16 

15 

16 

16 

15 

15 

169 

169 

171 

169 

100 

105 

101 

130 

132 

1 33 

L63 

165 

163 

168 

166 

269 

288 

280 

27!) 

276 

270 

281 

269 

291 



INDEX 435 



Page 
Concrete work, machinery for 

plant for street work 292 

plant for ten-story building 289 

. wood-working plant 288 

Conglomerates 8 

Coping 84 

Corbel : 84 

Counter fort 85 

Coursed masonry 85 

Coursed rubble 85 

Coursing joint 360 

Cramp 85 

Crandall 85 

Cribs 139 

Crown 360 

Crushing strength of brick 13 

Crushing strength of stone ' 2 

Culverts 158, 247 

arch 163, 248 

box 247 

double box 161 

end walls 162 

plain concrete 163 

stone box 158 

Curbing 169 

Curtain walls 246 

Gushing pile foundation 135 

D 

Depositing concrete under water 107 

methods " ■. 102 

bags 103 

buckets 102 

tubes" 103 

Diamond steel bar SO 

Dimension stone 85 

Disc piles 120 

Dolomite 7 

Double box culverts 161 

Dowel 85 

Draft 85 

Drop-hammer pile-driver 126 

Dry stone masonry 86 

E 

Elastic arches 396 

advantages and economy 396 

arch ribs, classification of 399 



436 INDEX 



Page 
Elastic arches 

complete solution of numerical problem 409 

intrados 408 

mathematical principles 399 

technical meaning 396 

weight and thickness of 407 

Electric motors 281 

Elliptical arch 362 

End walls 162 

English bond used in brick masonry 96 

Extrados 86, 360 

F 

Fire brick ._ 13 

Fire protection qualities of concrete 70 

Baltimore fire 72 

cinder vs. stone concrete 71 

theory 71 

thickness of concrete required 71 

Flemish bond 96 

Footing 86, 112, 231 

beam 115 

calculation of 113 

continuous beams 236 

pier 116 

simple 231 

steel I-beam 116 

Forms . 297 

adjustable clamp for 307 

for beams and slabs 300 

Blair steel 309 

for columns 298 

for conduits and sewers 308 

cost of, for buildings 302 

cost of, for garage 305 

for Locust Realty Co. building 301 

for Torredale filters 308 

for walls 310 

Foundations 105 

bearing power of soil 107 

caissons 140 

cofferdams 138 

cribs 139 

footings 1 12 

pile H9 

preparing bed 

on firm earth 1 10 

on rock 110 



INDEX 



437 



T7 1 *• Page 

Foundations 

preparing bed 

on wet ground Ill 

subsoil 106 

Friction crab hoist 281 

G 

Gang moulds 30 

Granite 8 

Gravel, cost of 51 

Gravity concrete mixers 271 

Grillage 135 

Grout 86 

H 

Haunch, definition of 360 

Heading joint 361 

Hercules cement stone machine 295 

Hinged arch ribs 425 

Hoisting buckets 284 

Hoisting concrete 280 

Hoisting lumber and steel 283 

Hunt bender 320 

Hydraulic lime 18 

Hydrostatic arch 362 

I 
Intrados 86, 361 

J 

Jamb 86 

Johnson steel bar 87 

Joints ■ 86 

K 

Kahn steel bar 80 

Keystone 361 

L 
Lime 

common 17 

hydraulic 18 

Limestone 6 

Lintel 87 

M 

McKelvey batch mixer . . 275 

Marble 6 

Masonry arches, constructive features of 360 



438 INDEX 



Page 

Masonry materials 1 

brick 9 

broken stone 39 

cementing materials ~. 17 

cinders -12 

concrete 47 

concrete building blocks J4 

mortar 42 

sand , 36 

stone 1 

Masonry and reinforced concrete 1-429 

Medusa waterproof compound GO 

.Mixers, concrete 270 

Mixing concrete 74 

by hand 74 

by machinery 75 

power for 279 

Modulus of elasticity of concrete . 50 

Mortar 42 

common lime 43 

natural cement 43 

Portland cement 44 

proportions of materials for 40 

re-mixing, effect of ' 45 

Motors for. operating mixers or hoists 282 

N 

Natural cement 34 

constancy of volume 34 

definition 34 

fineness 34 

specific gravity 34 

tensile strength 34 

time of setting 34 

P 

Parapet 36 1 

Pier footings, design of IK) 

Piers 153 

Pile caps 128 

Pile-drivers 126 

Pile foundations. 11!) 

cost 1 36 

cushing 135 

finishing 12!) 

grillage 1 35 

piles. 11!) 

for sea-wall a1 Annapolis 137 



INDEX 



439 



Page 
Pile foundations 

steel sections 119 

Piles : 119 

bearing power of 123 

cast-iron 119 

for Charles River dam 136 

concrete ' 130 

disc 120 

driving, methods of 12G 

reinforced concrete 130 

sawing off * : 129 

screw 120 

sheet 120 

splicing 128 

steel 133 

wooden bearing ' 122 

Pitched-faced masonry 87 

Pitching chisel 87 

Plinth 87 

Plug 87 

Pneumatic caissons 143 

Pointed arch . 362 

Pointing 88 

Portland cement 20, 34 

constancy of volume 35 

definition 34 

fineness 35 

specific gravity 35 

sulphuric acid and magnesia 35 

tensile strength 35 

testing machines 35 

time of setting 35 

Portland cement mortar 44 

Pozzuolana 19 

Puddling , - 105 

Q 

Quarry examinations of stone G 

Quarry-faced stone 88 

Quoin 89 

R 

Ramming concrete 58 

Ransome steel bar 79 

Raymond concrete pile 132 

Reinforced concrete 173 

acid treatment 205 

bending bars 318' 



440 INDEX 



Page 

Reinforced concrete 

bond required in bars, computation of 202 

cast slab veneer 266 

centers for arches 311 

colors for finish 267 

columns ' 7 ..*.... 7 248 

compressive forces, center of gravity of 183 

compressive forces, summation of 181 

culverts 247 

dry mortar finish 265 

economy of, for compression 176 

efflorescence 268 

elasticity of, in compression 177 

finish for floors 268 

flexure, theory of ... . 173 

footings 231 

forms for 297 

granolithic finish : 264 

masonry facing 263 

moduli, ratio of 185 

mortar facing 262 

mouldings 266 

neutral axis, position of '.' 183 

ornamental shapes 266 

painting concrete surface 267 

plain beam, detailed design of ' 208 

plastering 261 

resistance to slipping of steel in concrete 199 

resisting moment 186 

retaining walls 238 

slabs on I-beams 211 

spacing slab bars 198 

statics of plain beams 174 

steel, economy of for tension 176 

steel, effect of quality of 210 

steel, percentage of 185 

stone or brick facing 263 

straight-line formula; 192 

tanks 256 

tee-beams 214 

temperature cracks, reinforcement against 212 

theoretical assumptions 179 

transporting 286 

vertical shears, distribution of 204 

vertical walls 246 

wind bracing 244 

Reinforced-concrete arches, description of two 428 



INDEX 441 



Page 
Reinforced-concrete work 

apartment house 339 

Bronx sewer, N. Y 349 

Buck building .' 326 

Erben-Harding Co. building 333 

Fridenberg building 344 

General Electric Co. building 345 

girder bridge 349 

McGraw building 343 

McNulty building 341 

main intercepting sewer 346 

Mershon building 330 

Swarthmore shop building 337 

water-basin and circular tanks 346 

Reinforcing steel 76 

expanded metal 81 

quality of 76 

types of : .- 78 

deformed bars 78 

plain bars , 78 

structural 78 

wire fabric 81 

Relieving arch 362 

Retaining walls 145, 238 

base-plate . 240 

buttresses 241 

empirical rules 151 

failure of 148, 152 

L-shaped 243 

resultant pressure of 148 

theoretical formulae 146 

Right arch 362 

Ring stone 361 

Rip-rap 89 

Rosendale cement 19 

Rotary concrete mixers 274 

Rubble 89 

Rubble concrete 51, 101 

depositing under water 102 

materials, quantities of 102 

stone, proportion and size of 101 



Safe loads on wooden columns 315 

Safe stresses in lumber for wooden forms 313 

Sand 36 

cleanness 38 

coarseness 37 



442 INDEX 



Page 
Sand 

cost of ; 51 

essential qualities 37 

geological character 37 

object 37 

percentage of voids 39 

sharpness 37 

Sand-lime brick 14 

Sandstone 7 

Sand washing 295 

Screw piles 120 

Segmental arch 362 

Semicircular arch 362 

Shearing strength of concrete 50 

Sheet piles 120 

Simplex concrete pile 133 

Skew arch : .' 362 

Skewbacks . . . 361 

Slab bars 321 

Slag cement ' 19 

Slope-wall masonry ' 89 

Soffit 361 

Spalls 89 

Span : 361 

Spandrel 361 

Specific gravity of cement 23 

Springer _ ' 362 

Springing line 362 

Squared-stone masonry 89 

Steam-hammer pile-driver 127 

Steel, preservation -of in concrete 68 

Steel for reinforcing concrete 76 

Steel bars 

diamond 80 

Johnson •• 79 

Kahn 80 

Ransome 79 

Thacher , 79 

twisted lug 80 

Stool I-beam footings 116 

Stool piles 133 

Steel wire fabric reinforcement 81 

Stone 1 

appearance 3 

building • • 6 

characteristics 1 

cost 1 

durability 2 



INDEX 443 



Page 
Stone 

seasoning of 9 

strength 2 

testing 3 

Stone arch 429 

Stone box culverts ' 158 

Stone dressing .- . . . 91 

cost of 93 

Stone masonry 83 

allowable unit-pressures 94 

bonding 93 

classification of dressed stones 90 

cost of 95 

cutting and dressing stone 91 

definitions 83 

mortar, amount of 94 

Stone testing 3 

absorption 4 

chemical 4 

frost 4 

physical 5 

quarry examinations . . . 6 

String-course ' . 89, 362 

Structural steel 78 

Subsoil, classification of 100 

Sylvester process of waterproofing 63 

T 
Tables 

allowable pressures on masonry - 95 

barrels of Portland cement per cu. yd. of mortar 55 

beam data 219 

brick and mortar, quantities of 99 

building stone, physical properties of 10 

cement, sand, and stone in actual structures, proportions of 54 

colored mortars 267 

concrete, compressive strength of 49 

concrete, compressive tests of 50 

concrete, ingredients in one cu. yd. of 55 

concrete, tensile tests of 76 

elastic arch data 406 

expanded metal, standard sizes of 81 

footings, ratio of offset to thickness for 114 

Lambert hoisting engines, sizes of 282 

modulus of elasticity of some grades of concrete 185 

mortar per cu. yd. of masonry 185 

parabolic formulae 185 

Ransome engines, dimensions for 280 

rectangular beam computation 200 



JAfr' 13 \bCl 



444 INDEX 



Tables Page 

retaining walls, thickness of 151 

safe loads for beams 313 

slab computation 197 

square and round steel bars, weights and areas of 82 

straight-line formula? 193 

strength of solid wooden columns 314 

voussoir data 371 

water, percentage of, for standard sand mortars 27 

Tanks, reinforced-concrete 256 

design 256 

over-turning, test for 257 

Tee-beams 214 

approximate formulae 221 

flange, width of 217 

numerical illustrations of 219 

rib, width of 218 

resisting moment of 215 

shear in 225 

shearing stresses between beam and slab 222 

Template 89 

Tensile strength of cement 32 

Tensile strength of concrete 50 

Testing cement 21 

Testing stone 3 

absorption 4 

chemical 4 

for frost 4 

physical 5 

quarry examinations " 6 

Thacher steel bar 79 

Transporting concrete 286 

Trap rock 8 

Twisted lug bar SO 

V 

Vicat needle 20 

Voussoir arches 303-396 

Voussoirs 362 

W 

Waterproof compound, Medusa , 66 

Waterproofing 

asphalt 64 

felt laid with asphalt 65 

Sylvester process 63 

Water-table 89 

Water-tightness of concrete 61 

Wetness of concrete 06 

Wind bracing 244 

Wooden bearing piles 124 



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